Start by making the cake. Preheat oven to 425ºF. Line two 12½ x 15½-inch jelly roll pans with parchment and brush with melted butter.

In the bowl of stand mixer fitted with the whisk attachment, beat the egg whites until soft peaks form. Beat in the granulated sugar and continue beating until the peaks are stiff and glossy. Gently scrape into a medium bowl and set aside.

Replace the whisk with the paddle attachment. Beat the ground almonds, confectioners sugar and whole eggs on medium speed until light and airy, about 3 minutes. Reduce speed to low and gradually mix in flour, mixing just until incorporated. Using a rubber spatula, gently fold in the meringue, then the melted butter. Divide the batter evenly among the two pans (I think it was about 600 grams of batter per pan) and spread to cover the entire surface.

Bake cakes for 5-7 minutes, until light brown and springy to the touch.

Place a sheet of parchment over each pan, then carefully turn the cakes over to unmold. Carefully peel off the layer of parchment on the bottom, turn it over and use it to cover the cakes. Let cool to room temperature. Cakes can be made up to 1 day in advance, cooled, wrapped and stored at room temperature.

While the cakes are cooling, prepare the espresso syrup by combining all the ingredients in a small saucepan. Bring to a boil, then remove from heat and set aside to cool. The syrup can be made up to 1 week in advance and stored in the refrigerator.

To make the buttercream, dissolve the espresso in the boiling water and set aside. Beat the egg and egg yolk on medium-high speed in the bowl of a stand mixer fitted with the whisk attachment until pale and foamy.

Bring the sugar, water and vanilla bean paste to a boil in a small saucepan. Stir only until the sugar dissolves. Continue cooking, without stirring, until the mixture reaches 255ºF. With the mixer running on low speed, slowly pour in the syrup. Don’t be concerned if some of it sticks to the sides of the bowl. Increase speed to medium-high and continue beating until the eggs are thick, satiny and room temperature, about 5 minutes.

With the mixer on medium speed, steadily add the butter in 2-tablespoon increments. Once all the butter has been added, increase speed to high and beat until the buttercream has thickened slightly. Beat in the dissolved espresso.

Chill, stirring frequently, until the buttercream is firm enough to be spread, at least 30 minutes. If making ahead of time, the buttercream can be refrigerated for 4 days or frozen up to a month. Bring to room temperature before using and beat to smooth it.

To make the ganache, place the chocolate in a medium bowl. Bring the milk and cream to a boil, then pour over the chocolate. Wait 1 minute, then stir until smooth and glossy. Add the butter, 2 tablespoons at a time, and continue stirring until the ganache is smooth.

Refrigerate, stirring every 5 minutes, until the ganache thickens to a spreadable consistency, about 20 minutes. The ganache can be refrigerated 3 days or frozen up to a month. Bring to room temperature before using.

To assemble the cake, line a baking sheet with parchment or wax paper. Working with one cake a time, cut each cake into one 10×10-inch square and one 10×5-inch rectangle. Place one square of cake on the parchment and use a pastry brush to moisten with the espresso syrup. Spread about ¾ of the buttercream onto the cake, making sure to spread evenly. If the buttercream is too soft, you can freeze the cake for about 10 minutes before proceeding.

Top with the two rectangular pieces of cake, placing them side by side to form a square. Moisten with the syrup and top with ganache, making sure to spread it in an even layer. Top with the remaining cake layer, moisten, then freeze for 10 minutes. Top with a thin layer of buttercream. This is just to smooth the top and prepare it for the glaze, so less is more here. Refrigerate for at least 1 hour or up to 6. If you’re in a hurry, you can freeze the cake for 20 minutes before continuing.

When you’re ready to glaze the cake, bring the butter to boil in a small saucepan. Remove from heat and skim off the top foam to clarify the butter. Pour the clear yellow butter into a small bowl and discard any milky residue.

Melt the chocolate in a medium bowl over simmering water, then stir in the clarified butter. Lift the chilled cake off the parchment lined pan and place on a rack set atop the parchment lined pan. Pour the glaze over the cake, using a long offset spatula to help smooth it evenly across the top. Though messy, I would recommend transferring the cake to a cake stand or serving dish now, so that the set glaze doesn’t crack when you lift the cake later on.

Refrigerate until glaze is set and cake is chilled. Use a long, thin knife that has been dipped in very hot water and wiped dry to cut the sides of the cake, removing any drips from the glaze and exposing the layers. A hot knife works best to slice this cake, which should be served slightly chilled.