For the sponge cake

1. Prep oven and pan. Heat oven to 425 degrees F. Butter a 15×10-inch rimmed baking pan, then line bottom of the pan with a sheet of parchment paper, leaving a 1-inch overhang on short sides. Generously butter the parchment paper and then dust the pan with cake flour, knocking out excess. Set aside.
2. Start batter. Beat whole eggs in a large bowl with a handheld electric mixer at high speed until eggs have tripled in volume and form a ribbon when beaters are lifted, 5 to 10 minutes. Reduce speed to low, then add almond flour and confectioners sugar and mix until just combined. Fold in cake flour. Set aside.
3. Prep egg whites. Beat egg whites in a bowl with cleaned beaters at medium speed until foamy. Add cream of tartar and salt and beat until whites hold soft peaks. Add granulated sugar, then increase speed to high and beat until whites just hold stiff peaks.
4. Fold together. Fold one third of the beaten whites into almond mixture to lighten, then fold in remaining whites. Fold in melted butter.
5. Fill pan. Pour batter into prepared baking pan. Using an offset spatula, gently spread the batter in the pan until it is even, being careful not to deflate. Batter will be about 1/4 inch thick in the pan.
6. Bake. Bake sponge cake until the top is very pale golden, 8 to 10 minutes, then cool in pan on a rack while preparing the coffee syrup, buttercream and chocolate glaze.

For the coffee syrup

1. Dissolve espresso. Stir together espresso powder and 1 tablespoon water until powder is dissolved. Set aside.
2. Make syrup. Bring sugar and remaining 1/2 cup water to a boil in a small saucepan, stirring until sugar is dissolved. Reduce heat and simmer syrup, without stirring for 5 minutes. Remove from heat and stir in Cognac and coffee mixture.

For the coffee buttercream

1. Dissolve espresso. Stir together espresso powder and 1 tablespoon water until powder is dissolved. Set aside.
2. Cook sugar. Bring sugar and remaining 1/4 cup water to a boil in a very small heavy saucepan, stirring until sugar is dissolved. Boil, without stirring until syrup registers 238 degrees on a thermometer.
3. Beat yolks. While syrup boils, beat yolks in a large bowl with cleaned beaters at medium speed for 1 minute.
4. Mix together. When sugar syrup reaches the correct temperature, with the mixer running at medium speed, add the hot syrup to the beaten egg yolks in a slow, steady stream (try to avoid beaters and side of bowl), then add coffee mixture and continue beating until mixture is completely cool, 3 to 5 minutes. Beat in butter, 1 piece at a time, and until buttercream is thickened and smooth.

For the the chocolate glaze

1. Melt chocolate and butter. Put the butter and chocolate in a microwave safe bowl. Microwave for 1 minute on high power and then stir the mixture together. If there are still chunks of unmelted chocolate, microwave the mixture again for 30 seconds and stir to combine. Continue microwaving the mixture in short increments and stirring until all the chocolate is melted and the mixture is smooth.
2. Cool. Cool the glaze until it reaches room temperature but is still liquid.

To assemble the cake

1. Cut cake. Loosen edges of the cake from the pan with the tip of a small knife, then using the parchment paper overhang, lift the cake from the pan and transfer the cake (on paper) to a cutting board. Trim outside edges of the cake. Cut cake into strips and squares (see Notes for measurements).
2. Cake layer 1. Put 1 cake square on a cake plate, then brush generously with one third of coffee syrup (about 1/4 cup). Spread half of buttercream evenly over top with an offset spatula, spreading to edges.
3. Cake layer 2. Arrange the 2 rectangular cake strips side by side on top of the cake to make a square, then brush with half of the remaining coffee syrup. Spread half of glaze evenly over top, spreading just to the edges.
4. Cake layer 3. Top with remaining cake square and brush with remaining coffee syrup. Spread remaining buttercream evenly over top, spreading just to edges. Chill cake until buttercream is firm, about 30 minutes.
5. Warm glaze. Reheat remaining glaze, if necessary, until it is shiny and spreadable (but not warm to the touch).
6. Glaze cake. Pour glaze over top layer of cake and spread evenly just to the edges. Chill cake until glaze is set, about 30 minutes, then trim edges slightly with a sharp serrated knife if you want neat edges.