Prep your pans and tools. Line two rimmed baking sheets (about 13x18 inches) with parchment.
Lightly grease and dust with flour. Set oven to 400°F (200°C). Have a candy thermometer ready for the buttercream.
Make the blackberry syrup. In a small saucepan, simmer blackberries, sugar, lemon juice, and water for 8–10 minutes.
Mash, then strain to remove seeds. Return to heat and reduce until slightly thick and syrupy. Cool completely.
You’ll use this to brush the sponge and to flavor the buttercream.
Mix the almond sponge base. In a bowl, whisk almond flour, powdered sugar, all-purpose flour, whole eggs, vanilla, and a pinch of salt until smooth and pale. The batter should ribbon off the whisk.
Whip the egg whites. In a clean bowl, beat egg whites to soft peaks, then slowly add granulated sugar and whip to glossy medium-stiff peaks.
Combine and finish the sponge. Fold a third of the whites into the almond batter to loosen, then fold in the rest gently. Stream in melted butter and fold just to combine.
Do not overmix.
Bake the sponge in thin sheets. Divide batter between pans and spread into even layers (use an offset spatula). Bake 6–8 minutes until light golden at the edges. Cool completely, then run a knife along the sides and lift out the sheets using the parchment.
Make the Italian-style buttercream base. In a stand mixer, beat egg yolks on medium until thick and pale.
Meanwhile, heat sugar and water to 238°F (114°C), the soft-ball stage. With the mixer running, stream the hot syrup down the side of the bowl into the yolks. Beat until the bowl is cool to the touch.
Add butter and flavors. Beat in room-temperature butter, a tablespoon at a time, until smooth and fluffy.
Mix in cooled espresso, 2–4 tablespoons blackberry syrup or puree, vanilla, and a pinch of salt. Adjust to taste: more blackberry for fruitiness, more coffee for depth.
Make the ganache. Heat cream to a simmer, pour over chopped dark chocolate, let sit 1–2 minutes, then stir until silky. Add a teaspoon of neutral oil or a small knob of butter for extra shine, if you like.
Let thicken to a spreadable consistency.
Trim the sponge layers. Use a ruler to cut three neat rectangles of sponge, about 10x12 inches each. You can reassemble offcuts if needed; just keep layers even.
Assemble: first layer. Place the first sponge on a board lined with parchment. Brush generously with blackberry syrup—don’t soak it, but be thorough. Spread a thin, even layer of buttercream (about 1/4 inch).
Chill 5–10 minutes to set.
Second layer. Add the second sponge, brush with syrup, then spread a thin layer of ganache. Chill again until just firm.
Third layer. Top with the final sponge and brush lightly with syrup. Finish with a smooth layer of buttercream over the top and sides for sharp edges.
Chill 20 minutes.
Final glaze. Warm the remaining ganache until pourable but not hot. Pour over the chilled cake and smooth quickly with an offset spatula. Tap the board gently to settle the glaze. Chill until set.
Clean edges and decorate. For sharp sides, warm a knife in hot water, wipe dry, and trim edges.
Garnish with fresh blackberries and, if you want a luxe touch, a bit of gold leaf.
Slice and serve. Use a hot, dry knife for each cut to keep layers pristine. Serve slightly cool, not cold, so the buttercream is silky.