Preheat the oven to 350°F Butter a 9-inch round cake pan. Dust the pan with flour and tap out the excess.
Whisk together the flour and cocoa powder in a medium bowl; set aside.
Fill a pot one-third full with water and bring to a simmer. Combine the eggs and sugar in the bowl of an electric mixer. Place the bowl over the simmering water and whisk until the mixture is warm to the touch. Transfer the bowl to the mixer stand and, using the whisk attachment, beat on medium speed until the mixture triples in volume and forms a thick ribbon when the whisk is lifted, about 8 minutes. Using a large rubber spatula, gently fold in the flour mixture. Fold in the melted butter. Scrape the batter into the pan and smooth the top.
Bake the cake for 20 to 25 minutes, until it has pulled away from the side of the pan and the top springs back when lightly touched. Cool the cake in the pan for 10 minutes. Unmold the cake on a rack and cool completely, right side up.
In the bowl of an electric mixer, using the whisk attachment, beat 2 1/2 cups of the heavy cream to soft peaks. Scrape half of the whipped cream into a medium bowl. Cover both bowls and refrigerate.
Place the dark chocolate in a large bowls. Bring the remaining 1 cup cream to a boil in a small saucepan. Pour the hot cream over the dark chocolate and set aside till it melts. Once it's nearly melted start gently the mixture until smooth.
Let the chocolate mixtures cool for 10 minutes, then fold the chocolate into the remaining whipped cream.
Combine 1/4 cup water and 1/2 cup sugar in a small saucepan. Bring to a boil over medium-high heat, stirring to dissolve the sugar, then mix in the Raspberry Liqueur. Let the syrup cool to room temperature.
Using a serrated knife, slice the cake horizontally in half. Cup a strip of parchment paper to line the inside of a 9x4-inch cake ring. Line the mold with the strip and place it on a serving plate. Place a 9-inch cardboard cake round in the bottom of the cake ring. Place the bottom cake round, cut side up, in the ring. Brush the cake generously with the Raspberry syrup. Scrape the dark chocolate mousse onto the cake and smooth it into an even layer. Top with the second cake round, cut side down. Brush the cake generously with Raspberry syrup. Chill the cake for at least 2 hours and up to 24 hours.
To unmold the cake, lift it off the plate, holding it with your palm against the cardboard round. Using a hairdryer or warm damp towel, briefly warm the cake ring mold. Lift off the ring mold and peel off the parchment strip. Allow the cake to stand at room temperature for 30 minutes before serving.