We developed this recipe using Softasilk Cake Flour. When making the frosting, let the chocolate cool to between 85 and 100 degrees before adding it to the butter mixture. The frosting can be refrigerated, covered, for up to 3 days. Let it stand at room temperature for 1 hour before using.
1. For the cake: Adjust oven rack to middle position and heat oven to 350 degrees. Grease three 8-inch round cake pans, line with parchment paper, grease parchment, and flour pans. Whisk flour, baking powder, and salt together in small bowl.
2. Process sugar, eggs, almonds, vanilla, and almond extract in food processor until combined, about 10 seconds. With processor running, add melted butter in steady stream until incorporated. Transfer sugar mixture to large bowl.
3. Sift flour mixture over sugar mixture in 3 additions, whisking to combine after each addition until few streaks of flour remain. Continue to gently whisk batter until almost no lumps remain.
4. Transfer one-third of batter (about 1¾ cups) to 1 prepared pan and smooth top with rubber spatula. Divide remaining batter evenly between 2 bowls. Add green food coloring to 1 bowl and mix until combined. Whisk cocoa, water, and red food coloring in small bowl until smooth. Add red food coloring mixture to second bowl of batter and mix until combined. Transfer colored cake batters to remaining 2 prepared pans and smooth tops with rubber spatula.
5. Bake until toothpick inserted in centers comes out clean, 24 to 28 minutes, rotating pans halfway through baking. Let cakes cool in pans on wire rack for 10 minutes. Run paring knife around edges of pans to loosen. Remove cakes from pans, discarding parchment, and let cool completely on rack, about 2 hours.
6. For the frosting: Process butter, sugar, cocoa, and salt in food processor until smooth, about 30 seconds, scraping down sides of bowl as needed. Add corn syrup and vanilla and process until just combined, 5 to 10 seconds, scraping down sides of bowl as needed. Add chocolate and process until smooth and creamy, 10 to 15 seconds. (Frosting can be held at room temperature for up to 3 hours.)
7. Place red cake layer on cake plate or pedestal. Spread 1/3 cup jam evenly over cake, leaving ¼-inch border. Top with white cake layer, press lightly to adhere, then spread remaining 1/3 cup jam evenly over cake, leaving ¼-inch border. Top with green cake layer and press lightly to adhere. Spread about 1 cup frosting evenly over top and sides of cake, making sure to fill in gaps between cake layers to create smooth sides. Refrigerate cake until frosting is firm to touch, about 1 hour. Spread remaining frosting evenly over top and sides of cake.
8. Starting in middle of top of cake, lightly press back of spoon into frosting and swoop up to create C shape. Continue swoops outward in concentric circles to edge of cake. Serve.