
Preheat the oven to 350° with oven racks in the upper and lower third. Lightly grease 3 9-by-13-inch baking pans or quarter sheet pans (9-by-13-inch) with nonstick baking spray; line the bottoms with parchment paper. Set aside.
Beat the butter and 1 3/4 cups of the sugar on medium speed until well combined in the bowl of a stand mixer fitted with a paddle attachment, about 3 minutes. With the mixer on medium speed, add the egg yolks, one at a time, beating well after each addition. Stir in the almond extract and salt. With the mixer on low, gradually add the flour, and beat until just combined. Set aside.
Beat the egg whites with a handheld mixer on medium-high speed until foamy in a large bowl, about 30 seconds. Continue beating, gradually adding the remaining 1 1/2 tablespoons of the sugar, and beating until the stiff peaks form, 1 to 2 minutes.
Fold one third of the egg whites into the batter with a rubber spatula, until just combined. Fold in the remaining egg whites just until the batter is smooth and fully combined.
Divide the batter evenly among 3 medium bowls. Add 3 to 4 drops of red food coloring to the first bowl, 3 to 4 drops of green food coloring to the second bowl, and leave the third bowl white. Fold the food color to evenly color each batter.
Spread each batter in the prepared baking pans, keeping colors separate. Bake until the cakes are set and dry on top, 14 to 16 minutes. Cool the cakes completely in the pans, about 30 minutes.
Turn the green cake layer out onto a parchment paper-lined baking sheet; peel off parchment paper on the bottom side of the cake and discard. Spread top of the cake evenly with 1/3 cup of the jam. Invert the white cake layer directly on top; discard parchment paper. Spread the top of the white cake layer evenly with the remaining ⅓ cup of the jam. Invert the red cake layer directly on top; discard parchment paper. Cover the top and sides of the cake with plastic wrap. Chill at least 30 minutes or overnight.
Unwrap the cake. Place chocolate in a medium microwave-safe bowl. Microwave in 30-second intervals, stirring in between each, until the chocolate is almost smooth with some unmelted bits remaining. Remove the chocolate from the microwave. Stir until the residual heat fully melts chocolate and the mixture is smooth (microwave an additional 15 seconds, if needed).
Spread about half of the melted chocolate evenly over the top of the cake. Refrigerate until the chocolate is set, about 30 minutes.
Invert the cake onto a cutting board and discard the parchment paper. Remelt the remaining chocolate in 15 second intervals until smooth. Spread the chocolate evenly over the top of the cake. Using a fork, create long wavy patterns longs across the chocolate. Chill until the chocolate is set, about 30 minutes.
Warm a large chef's knife under hot water, and dry. Cut the cake into about 24 pieces, warming the knife after each slice.