Step 1: Preheat oven to 425°F (220°C). Line two half-sheet pans (13x18 inches) with parchment paper. Create a parchment sling on each for easy removal.
Step 2: In a large bowl, whisk egg whites and cream of tartar until soft peaks form. Gradually add 1/4 cup granulated sugar, whipping until stiff, glossy peaks form. Set aside.
Step 3: In another large bowl, whisk egg yolks, 1/2 cup granulated sugar, and melted butter until pale and thick.
Step 4: Gently fold almond flour and all-purpose flour into the yolk mixture until just combined.
Step 5: Carefully fold one-third of the whipped egg whites into the almond mixture to lighten it, then gently fold in the remaining whites in two additions until no streaks remain.
Step 6: Divide batter evenly between prepared sheet pans, spreading into thin, even layers. Bake 5-7 minutes, until lightly golden and set. Let cool completely. Trim the cooled cakes to create three uniform 8x12 inch rectangles.
Step 7: For the coffee syrup: In a small saucepan, combine 1 cup strong coffee, 1/2 cup granulated sugar, and coffee liqueur (if using). Bring to a simmer, stirring until sugar dissolves. Remove from heat and let cool.
Step 8: For the coffee buttercream: In a heatproof bowl over simmering water, whisk 5 egg whites and 1 cup granulated sugar until sugar dissolves and mixture reaches 160°F (71°C).
Step 9: Remove from heat. Transfer to a stand mixer and beat on high until stiff, glossy peaks form and meringue is cool to the touch (about 10 minutes).
Step 10: Switch to paddle attachment. With mixer on medium-low, gradually add softened butter, one piece at a time. Beat until smooth, light, and fluffy.
Step 11: Add cooled espresso and vanilla extract; beat until combined.
Step 12: For the chocolate ganache: Place chopped dark chocolate in a heatproof bowl. Heat heavy cream until simmering; pour over chocolate. Let sit 5 minutes, then whisk until smooth. Stir in softened butter. Let cool to a spreadable consistency.
Step 13: To assemble: Place one joconde sponge layer on a serving platter. Brush generously with coffee syrup.
Step 14: Spread about half of the chocolate ganache evenly over the first sponge layer. Chill for 10-15 minutes to set.
Step 15: Carefully place the second joconde sponge layer on top. Brush generously with coffee syrup.
Step 16: Spread about half of the coffee buttercream evenly over the second sponge layer. Chill for 10-15 minutes to set.
Step 17: Place the third joconde sponge layer on top. Brush generously with coffee syrup.
Step 18: Spread remaining coffee buttercream over the top and sides for a crumb coat. Chill for 30 minutes until firm.
Step 19: Spread the remaining ganache evenly over the top of the chilled cake. Chill again for 30 minutes.
Step 20: For the mirror glaze: In a small saucepan, combine 1/2 cup heavy cream, 1/4 cup water, 1/4 cup granulated sugar, and cocoa powder. Whisk until smooth; bring to a gentle simmer. Remove from heat and stir in chopped dark chocolate until melted and smooth. Pass through a fine-mesh sieve. Let cool to about 90°F (32°C).
Step 21: Place chilled cake on a wire rack over a baking sheet. Pour cooled mirror glaze evenly over the cake, letting it drip down the sides. Let set for 15-20 minutes.
Step 22: Once glaze is set, carefully trim edges with a hot, dry knife for clean lines. Decorate with gold leaf or chocolate stencil if desired. Chill until ready to serve. For best flavor, let sit at room temperature for 15-30 minutes before serving.