Place the sliced almonds on a baking sheet and toast in the oven for about 5-7 minutes or until lightly browned and fragrant. Remove from oven and let cool.
Once completely cooled, place the nuts in a small food processor, along with 1 tablespoon of the cake flour, and process until finely ground.
Increase the oven temperature to 450°F.
Grease a 17 inch x 12 inch jelly roll pan, line with parchment, and then grease and flour the parchment paper. Set aside.
While eggs are still cold separate two of the eggs, placing the yolks in one large mixing bowl and the whites in another bowl.
To the two yolks, add the additional yolk, and the two remaining eggs.
Cover the two bowls with plastic wrap and allow the eggs to come to room temperature before using.
Meanwhile, in a small bowl whisk together the remaining 2 tablespoons of cake flour and the ground almonds. Set aside.
Add 1/2 cup sugar to the yolk mixture and beat on high speed for five minutes, or until pale, thick and fluffy. At this point beat in the vanilla extract.
Sift half the flour mixture over the egg yolk mixture and fold in gently with a rubber spatula, just until the flour is incorporated. Sift the remaining flour mixture over the batter and fold together.
In a large clean mixing bowl, beat the egg whites until foamy. Add the cream of tartar and continue beating until soft peaks form.
Beat in one tablespoon sugar and beat until stiff peaks form.
Gently fold a little of the whites into the batter to lighten it, and then fold in the rest of the whites. Pour the batter into the prepared pan, spreading the cake batter with an offset spatula.
Bake for 7 minutes or until golden brown.
Immediately upon removing the cake from the oven invert the sponge cake onto a clean dish towel that has been sprinkled with icing sugar.
Carefully remove the parchment paper, sprinkle the cake lightly icing sugar, and roll up the sponge, with the towel, while it is still hot and pliable.
Place on a wire rack to cool.
To make the cream filling place the whipping cream, vanilla extract, and sugar in a large bowl and stir to combine.
Cover and chill the bowl and beaters in the refrigerator for at least 30 minutes.
When chilled, beat the mixture until stiff peaks form.
Fold in 1/3 cup toasted ground almonds.
When ready to fill, unroll the sponge, spread with the filling, and reroll.
Transfer to a serving platter, cover, and chill in the refrigerator for a few hours or overnight.