Preheat: Heat the oven to 350°F. Butter two 9-inch round cake pans, line the bottoms with parchment paper, and butter the paper too.
Beat the yolks: In a large bowl, beat the 6 egg yolks with 3/4 cup of the sugar until pale and thick — about 3 minutes. Beat in the vanilla and the oil.
Whip the whites: In a clean bowl, beat the egg whites with the remaining 1/4 cup sugar until soft peaks form — the tip of the peak flops over gently when you lift the beater.
Fold in the dry ingredients: Sift the flour, cocoa, baking powder, and salt over the yolk mixture, then fold gently with a rubber spatula until just combined. A few streaks of flour are fine here.
Fold in the whites: Fold in a third of the whipped whites to loosen the batter, then fold in the rest with big, gentle strokes — down the middle, across the bottom, up the side, over the top. Stop the moment no white streaks remain.
Bake: Divide the batter between the pans and bake for 25 to 30 minutes. The cake is done when the center springs back completely under your fingers and the edges pull slightly away from the pan.
Cool and slice: Cool in the pans for 10 minutes, then turn the layers onto a wire rack and cool completely. Once fully cool, slice each layer in half horizontally with a serrated knife to make four thin layers.
Make the cherry filling: In a small saucepan, bring the cherries, 1/4 cup sugar, and lemon juice to a simmer. Whisk the cornstarch with 2 tablespoons of cold water, stir it into the pot, and cook for 3 to 4 minutes until glossy and thick — like a loose jam. Stir in the kirsch if using, then cool completely.
Make the syrup: Stir the cherry juice, 2 tablespoons of kirsch (or the almond extract swap), and 1 tablespoon of sugar together until the sugar dissolves.
Whip the cream: In a cold bowl with cold beaters, whip the heavy cream, powdered sugar, and vanilla until firm peaks form. The peaks should stand up straight, not flop over.
Assemble: Place the first layer cut-side up on your serving plate. Brush generously with syrup, spread about 3/4 cup of cream over it, and add a third of the cherry filling. Repeat with the remaining layers, brushing syrup between each and on top of the final layer.
Frost and chill: Spread the remaining cream smoothly over the sides and top. Refrigerate for at least 2 hours — overnight is even better — so the syrup travels through the sponge and the cream sets for clean slices.
Garnish and serve: Press chocolate shavings onto the sides, pile fresh cherries on top, and serve cold. The finished cake should feel cool and firm, with every layer visible when you cut.