Preheat the oven to 450°F (230°C) and line a 11x17-inch (28x43cm) baking sheet with parchment. Butter the paper and set aside.
With a stand or electric handheld mixer with whisk attachment, beat together the almond flour, powdered sugar, all-purpose flour, eggs, egg yolk and melted butter until combined.
In a separate bowl whisk egg whites until thick and frothy, then slowly add the sugar, one tablespoon at a time and whip to stiff, glossy peaks.
Fold the whipped whites gently into the almond flour mixture until evenly mixed and then spread onto the prepared baking sheet.
Bake for 5-7 minutes, until the cake springs back when pressed. Remove from the oven and let cool completely on the pan.
Once cooled, wrap carefully and refrigerate until ready to assemble. (The colder cake will be easier to handle).
Make The Coffee Syrup
In a small saucepan over low heat, whisk the water, brandy, sugar and espresso powder until the espresso powder and sugar is dissolved. Set aside to cool.
Make The Buttercream
Mix the espresso powder with 1 tablespoon of water. Set aside.
With a stand fitted with a whisk attachment or electric handheld mixer, beat the egg on medium speed until the yolks are thick and pale.
In a small saucepan fitted with a candy thermometer, heat the remaining ½ cup (4floz/120ml) water and sugar until it reaches the soft ball stage: 238°F (115°C). Immediately remove from the heat and transfer to a glass measuring cup to stop the cooking.
While beating constantly on high speed, pour the hot syrup over the egg yolks followed by the dissolved espresso powder and continue beating until completely cooled.
Switch to a paddle attachment if using a stand mixer and add the butter, one tablespoon at a time and then continue beating until the mixture looks like a smooth buttercream. Set aside.
Make The Chocolate Glaze
Combine the chocolate and butter in a small saucepan or microwave safe bowl and heat gently, until melted. Set aside to cool and thicken to a spreadable consistency.
Assemble The Cake
Remove the cake from the refrigerator and cut into even thirds. A ruler works well for this.
Place one layer of cake onto a small baking sheet or cutting board covered in a piece of parchment and brush all over with the coffee syrup.
Spread half of the buttercream evenly over the cake.
Place a second layer of cake over the buttercream and brush evenly with the coffee syrup.
Spread half of the chocolate glaze over the second cake layer.
Top with the final cake layer and brush with the coffee syrup.
Spread the remaining buttercream over the final layer.
Warm the remaining chocolate glaze until pourable but not hot. Pour and spread evenly over the top layer of cake. Refrigerate until firm.
Trim the sides to neaten the cake and then carefully transfer to a serving plate. Let sit at room temperature for a few hours before serving. Store leftovers in an airtight container in the refrigerator for up to 3 days.