Step 1: Prepare the Joconde (Almond Sponge Cake)

1. Preheat the oven: Preheat your oven to 400°F (200°C). Line three 10×15-inch baking sheets with parchment paper and lightly grease them.
2. Make the almond batter: In a large bowl, whisk together the almond flour, all-purpose flour, powdered sugar, and salt. Add the eggs and beat until the mixture is light and fluffy. Set aside.
3. Whip the egg whites: In a clean bowl, beat the egg whites with a hand or stand mixer on medium speed until foamy. Gradually add half of the granulated sugar and beat until stiff peaks form.
4. Combine the batters: Gently fold the whipped egg whites into the almond batter in three additions. Be careful not to deflate the mixture.
5. Bake the sponge layers: Divide the batter evenly among the prepared baking sheets, spreading it into a thin, even layer. Bake each layer for 7–9 minutes, or until the cake is golden and springs back when touched. Let the cakes cool completely before peeling off the parchment paper.

Step 2: Make the Coffee Syrup

1. Combine ingredients: In a small saucepan, combine the water, sugar, and instant coffee. Heat over medium heat, stirring until the sugar dissolves.
2. Cool the syrup: Remove from heat and let the syrup cool to room temperature.

Step 3: Prepare the Coffee Buttercream

1. Dissolve the coffee: In a small bowl, dissolve the instant coffee in 1 tablespoon of warm water. Set aside.
2. Make the sugar syrup: In a saucepan, combine the sugar and water. Heat over medium heat until the mixture reaches 240°F (115°C) on a candy thermometer.
3. Whip the egg yolks: In a mixing bowl, beat the egg yolks on medium speed. Slowly pour the hot sugar syrup into the yolks while beating continuously. Continue to whip until the mixture is thick and completely cool.
4. Add butter and coffee: Gradually add the softened butter, one tablespoon at a time, beating until smooth. Stir in the dissolved coffee.

Step 4: Prepare the Chocolate Ganache

1. Heat the cream: In a small saucepan, heat the heavy cream over medium heat until it just begins to simmer.
2. Melt the chocolate: Pour the hot cream over the chopped chocolate in a heatproof bowl. Let sit for 1 minute, then stir until smooth. Allow the ganache to cool slightly before using.

Step 5: Assemble the Opera Cake

1. Layer 1 (base): Place one sponge layer on a serving platter or cake board. Brush generously with coffee syrup. Spread a thin layer of coffee buttercream evenly over the top.
2. Layer 2: Add the second sponge layer on top, brush with coffee syrup, and spread the chocolate ganache evenly over the layer.
3. Layer 3: Add the third sponge layer, brush with coffee syrup, and spread a final layer of coffee buttercream on top. Smooth the surface as much as possible.
4. Chill: Refrigerate the cake for at least 30 minutes to set the layers.

Step 6: Add the Chocolate Glaze

1. Prepare the glaze: Melt the dark chocolate and vegetable oil together in a heatproof bowl over a pot of simmering water or in the microwave. Stir until smooth.
2. Glaze the cake: Pour the glaze over the chilled cake, spreading it into an even, glossy layer. Allow the glaze to set in the refrigerator for 15–20 minutes.

Step 7: Trim and Serve

1. Trim the edges: Use a sharp knife to trim the edges of the cake for a neat, clean presentation.
2. Slice and serve: Cut the cake into small, rectangular slices. Serve chilled or at room temperature.