Preheat the oven to 400°F (200°C). Line three 8 x 8-inch cake pans with parchment paper and set aside.

In a large bowl, whisk together 1 1/4 cups almond flour, 1 cup powdered sugar, and 1/4 cup all-purpose flour until evenly combined.

Add the 5 whole eggs to the dry ingredients and mix gently until combined and smooth.

In a separate clean bowl, add 5 egg whites and 1/4 teaspoon salt. Beat on medium speed until soft peaks form. With the mixer running, add 2 tablespoons sugar and continue beating until stiff, glossy peaks form.

Fold the beaten egg whites into the almond-and-egg mixture in two additions, using a spatula and folding gently to keep the batter airy.

Fold in 2 tablespoons melted butter until just incorporated. Divide the batter evenly between the three prepared pans and smooth the tops.

Bake the cakes for 9–10 minutes, or until a skewer inserted in the center comes out clean. Remove from the oven and let the cakes cool completely in the pans. When cool, remove cakes from pans and peel off the parchment.

Make the coffee syrup: in a small saucepan combine 2/3 cup water, 1/2 cup sugar, and 3 teaspoons instant coffee. Heat over low to medium heat, stirring until the sugar and coffee dissolve and the syrup just comes to a simmer. Remove from heat, stir in 1/4 cup Cointreau if using, and let the syrup cool to room temperature.

Make the chocolate ganache for the filling: place 1 cup chopped chocolate in a heatproof bowl. Heat 3/4 cup heavy cream until it just begins to simmer, then pour the hot cream over the chopped chocolate. Let sit 1–2 minutes, then stir until smooth and glossy. Let the ganache cool to room temperature and thicken to a spreadable consistency.

Prepare the coffee buttercream: dissolve 1 1/2 teaspoons espresso powder in 1 1/2 tablespoons room-temperature milk and set aside. In the bowl of a stand mixer, cream 1 cup softened butter on medium-high speed until light and fluffy. With the mixer on low, add 3 1/2 cups powdered sugar gradually until incorporated, then add 2 teaspoons vanilla extract. Add the espresso-milk mixture and beat on medium speed until the buttercream is smooth and fluffy.

Assemble the cake: place one cake layer on a flat serving plate or board. Brush the top evenly with about one-quarter of the coffee syrup. Spread half of the coffee buttercream over that layer.

Place the second cake layer on top and brush it evenly with another quarter of the coffee syrup. Spread the cooled chocolate ganache over the second layer.

Place the third (top) cake layer on top, brush it with remaining coffee syrup, and spread the remaining coffee buttercream over the top and sides as desired. Cover the assembled cake and refrigerate for at least 2 hours to firm up.

Make the chocolate glaze: melt 2/3 cup chocolate in short bursts in the microwave (or over a double boiler) until smooth. Stir in 2 tablespoons coconut oil until the glaze is glossy. Reserve a small amount of glaze for piping decorations if you want to draw a musical note.

Place the chilled cake on a wire rack set over a sheet pan. Pour the remaining warm-but-not-hot glaze evenly over the top, letting some run down the sides. Refrigerate the cake until the glaze is set.

If desired, put the reserved glaze into a piping bag and pipe a musical note or other decoration on the set glaze. Store the finished cake refrigerated.