Preheat oven to 375F. Grease a 10x15" pan and line with parchment. Allow parchment to overhang the edges by a couple inches.
In a medium bowl, whisk flour, espresso powder, baking powder, and salt. Set aside.
In the bowl of a stand mixer, combine powdered sugar, 4 eggs, and vanilla. Whip until thick and pale. The whisk will leave tracks and ribbons will form if you drizzle the mixture onto itself. Mix in flour mixture and then the melted butter.
In a clean bowl of a stand mixer, begin to whip the egg whites on medium. When they start to foam, add the cream of tartar. Continue whipping while slowly adding the granulated sugar. Turn mixer to high and whisk until stiff peaks form.
Gently fold egg whites into the cake mixture. Pour into prepared pan and spread evenly. Bake for 5-10mins or until the cake springs back when pressed. Cool for 10mins before removing from pan.
Place sugar, espresso powder, and water into a small saucepan and bring to a boil. Simmer for 2mins. Remove from heat and stir in coffee liqueur. Cool completely.
Coffee French Buttercream
In a small bowl, combine espresso powder and hot water. Set aside.
Place sugar and water into a medium saucepan. Stir to combine but do not stir from this point forward. Insert a candy thermometer and cook until the mixture reaches 240F.
Meanwhile, using a stand mixer, whip egg yolks on high until thick, pale, and ribbons form.
When the sugar reaches 240F, remove from the heat. Turn mixer to medium and very slowly and carefully pour the sugar syrup into the yolks in a thin, steady stream.* Increase mixer to high and continue whip until the bowl is no longer warm to the touch (~10mins).
Switch to paddle attachment. Slowly add cubed butter and mix until smooth. Add the espresso mixture and whip until combined and the frosting is smooth.
Dark Chocolate Ganache
Finely chop chocolate and place into a bowl. Bring cream just barely to a simmer and pour over chopped chocolate. Cover with plastic wrap and let stand 2 mins. Stir with a spatula until combined and smooth. Allow to cool and thicken slightly before using on cake.
Using a 6" cake ring, cut out three cake rounds from the cake. Brush each with the coffee soak.
Place one cake round on a cake stand or serving plate. Spread with 1/3 cup of the ganache. Refrigerate until ganache sets. Spread with 1/2 cup of the french buttercream. Repeat with next layer.
Place last layer of cake on top. Frost the sides and top of the cake with the remaining frosting. Chill for 20mins.
Spread ganache over the top of the cake. Do a decorative border with remaining frosting if desired.
* The sweet spot for this is getting the stream right between the whisk and the sides of the bowl, so the syrup doesn't get splashed by the whisk.