FOR THE GENOISE: Preheat the oven to 350 degrees F and center a rack in the oven.
Butter a 9-inch round cake pan.
Dust with flour, tapping out the excess.
Pour a few inches of water into a skillet large enough to hold the bowl from your mixer.
Bring the water to a gentle simmer.
Melt the butter and set it aside to cool.
It should be just warm when you're ready for it.
Whisk the eggs and sugar together in the mixer bowl.
Place the bowl in the skillet of simmering water and, whisking without stop, heat the mixture until it is foamy, slightly pale, and reads between 130 and 140 degrees F on an instant-read thermometer, about 4 minutes.
Remove the bowl from the water.
Working in the mixer fitted with the whisk attachment, beat the mixture on high speed until it cools to room temperature and triples in volume.
When you lift the whisk, the batter will fall back into the bowl and form a ribbon that remains on the surface for 10 seconds before it dissolves, about 5 to 8 minutes.
Stir about 2 tablespoons of batter into the slightly cooled butter and set it aside.
With a large flexible rubber spatula, gently fold the flour into the batter in 2 or 3 additions, taking care to handle the batter gently in order to maintain its bubble structure.
(The batter will lose volume as you fold in the flour and later the butter. This reaction is inevitable and shouldn't jeopardize the success of the finished cake, but be careful just the same.) Still working with the spatula, fold in the butter mixture.
Pour the batter into the prepared pan and bake until the top is golden and springy to the touch and a toothpick inserted in the center of the cakes comes out clean, 28 to 33 minutes.
Transfer the cake to a cooling rack for 5 minutes.
Remove cake from pan, invert, and cool completely on the rack.
FOR THE SIMPLE SYRUP: Stir the sugar and water together in a heavy-bottomed saucepan, place over medium heat, and bring to the boil.
As soon as the syrup comes to the boil, remove it from the heat.
Cool to room temperature.
Using a serrated knife, cut 2 horizontally layers from cake, each 1/4-inch to 1/2-inch-thick.
PREPARE COFFEE SYRUP: Spoon off 2 tablespoons of the simple syrup, cover, and refrigerate for the glazed almonds.
Set the remainder of the syrup aside.
Line a strainer with a double thickness of dampened cheesecloth and place it over a small bowl; keep close at hand.
Bring the water to a boil in a medium saucepan.
Add the coffee, stir, and immediately pour the mixture through the lined strainer.
You should have about 3/4 cup of very dark coffee.
Stir in the instant coffee and the simple syrup.
Set the syrup aside until needed.
(The syrup can be made up to a week ahead and kept covered in the refrigerator.) PREPARE MOUSSE: Beat the cream until it holds medium-firm peaks, then cover and chill it until needed.
Place the eggs and yolks in the bowl of a mixer fitted with the whisk attachment and beat at the lowest speed for a few seconds, just to break up the eggs; set aside while you prepare the chocolate and sugar syrup.
Melt the chocolate in a microwave oven or in a metal bowl over a pan of simmering water.
Remove the chocolate from the heat and, if necessary, pour it into a bowl large enough to hold all the ingredients for the mousse.
Cool the chocolate to 114 degrees, as measured on an instant-read thermometer.
While the chocolate is melting and cooling, place the sugar and water in a small heavy-bottomed saucepan.
Bring the mixture to a boil, stirring occasionally and washing down the sides of the pan with a pastry brush dipped in cold water.
Boil the syrup over high heat without stirring it until it reaches 257 degrees F as measured on an instant-read thermometer, about 8 to 10 minutes, then immediately remove it from the heat.
With the mixer on the lowest speed, beat the eggs for a few seconds, then very slowly add the hot sugar syrup in a thin, steady stream.
To avoid splatters, try to pour the syrup down the side of the bowl, not into the spinning whisk.
(Inevitably, some will splatter, but don't attempt to scrape the hardened syrup into the eggs, you'll get lumps.) Increase the mixer speed to high and beat the eggs for about 5 minutes, or until they are pale and more than double their original volume.
If the mixture is still warm, reduce the speed to medium and continue to beat until the eggs are at room temperature.
Using a large rubber spatula, fold about 1/4 of the whipped cream into the chocolate.
Fold in the rest of the cream and then, very delicately, fold in the whipped egg mixture.
ASSEMBLY_ STAGE ONE: Center an 8 3/4-inch/22 cm dessert ring on a cardboard cake round.
Place 1 layer of genoise, cut side up, in the ring.
Brush enough coffee syrup over the cake to moisten it thoroughly.
Using an offset spatula or a flexible rubber spatula, spread 2 to 2 1/2 cups of mousse over the cake and smooth the top.
Position a second layer of cake on the mousse, pressing down gently and jiggling the cake to settle it in place.
Brush on some coffee soaking syrup and spread on another 2 to 2 1/2 cups of mousse; smooth the top level with the edge of the dessert ring.
You may have some syrup left over, and you will have extra mousse.
The syrup can be refrigerated for another use or discarded.
The mousse may be refrigerated for 2 days or frozen for a month.
Transfer the cake to the freezer and freeze for 2 hours to set the mousse.
The cake can be made to this point and frozen for up to 1 month.
If you're not going to freeze the cake for long-term storage, it should be transferred to the refrigerator to defrost after its 2 hour freeze. Remove the dessert ring. Using a long metal offset spatula, spread ganache over the top and sides of the cake. If you want to repeat with another one or two layers of ganache, go ahead—you’ve got plenty of ganache to play with. If the ganache is firm enough to hold a design, you can decorate the top now. If the ganache is still very soft, return the cake to the refrigerator for a few minutes to set it enough to hold a line drawn across its surface with a knife. (Keep the leftover ganache at hand so you can cover up any design attempts that don’t pass muster.) Decorate the top of the cake using the blade of a long, serrated bread knife. Hold the handle of the knife with one hand and the tip with the other. Starting at one edge of the cake and holding the knife almost perpendicular to the cake, gently slide the knife from one side of the cake to the other. Without “losing your place” at the edge of the cake, shift the blade about 1/16 inch and slide it 1/16 inch back to the opposite edge of the cake. You will have created the first V in a herringbone pattern. Continue until you have decorated the entire top of the cake. If the knife blade becomes clogged with ganache, clean the blade before continuing the pattern. Return the cake to the refrigerator for a few minutes to set the design. If you prefer, the cake can be finished with a flat-top—that is, a smooth coating of ganache—or you can decorate the top with swirls, ridges, or any other pattern that pleases you.
The last step is to press the toasted almonds against the sides of the cake. (If the ganache has set so it’s very firm and the almonds won���t stick to the sides, just warm the sides ever so slightly with a hair dryer—lightly melting the ganache will help the almonds to adhere.) The cake can be served now or chilled until serving time. If the cake is very cold and firm, let it rest at room temperature for 15 to 30 minutes before serving.
PREPARE ALMONDS: Center a rack in the oven and preheat the oven to 325 degrees.
Toss the almonds with the cocoa, then toss with the syrup to coat, and spread them out on a parchment-lined baking sheet.
Toast the almonds, stirring every 3 to 4 minutes, until they are deeply and evenly browned, about 10 to 12 minutes.
Transfer the sheet to a rack and cool the almonds to room temperature.
(The almonds can be used immediately or packed into an airtight container and stored at room temperature for about 4 days.) PREPARE GANACHE: Place the chocolate and cocoa in a medium bowl.
Bring the cream to a boil and remove it from the heat.
Pour the cream into the chocolate in three additions, using a rubber spatula to stir the mixture in concentric circles, starting each time with a small circle in the center of the bowl and working your way out into larger circles.
You'll have a smooth, glossy ganache.
Allow the ganache to rest uncovered and undisturbed (don't stir it) at room temperature until it sets, 40 to 60 minutes, depending on the room's temperature.
When the ganache is properly set, it will hold a ribbon for a second or two when stirred.
It is ready to be used now or covered and refrigerated until needed.
If the ganache is chilled, it must be brought back to its proper consistency by leaving it at room temperature until spreadable, or by heating it over hot water or in a microwave oven at low power.