Preheat and Prepare the Pan: Preheat the oven to 350°F. Line a half-sheet pan with parchment paper, leaving a slight overhang for easy removal.
Whip the Egg Whites: Add the egg whites to a stand mixer fitted with the whisk attachment. Begin whisking on low speed until foamy, then increase to medium-high speed.
Once soft peaks form, slowly stream in ¼ cup of the sugar. Continue whisking until the whites are stiff, glossy, and hold their shape. Transfer to a separate bowl and set aside.
Make the Almond Batter: Wipe out the mixing bowl and switch to the paddle attachment. Add the almond paste and remaining ¾ cup sugar. Beat until smooth and broken down, about 3 minutes.
Add the butter and beat until light and fluffy. Add the egg yolks and almond extract and beat until fully incorporated.
Add the Flour: Reduce speed to low and add the flour and salt. Mix just until combined.
Fold in the Egg Whites: Using a rubber spatula, gently fold half of the whipped egg whites into the almond batter to loosen it. Fold in the remaining egg whites until just incorporated, being careful not to deflate the batter.
Divide and Color the Batter: Divide the batter evenly into three bowls. Tint one bowl red, one green, and leave the third plain. Mix each gently until evenly colored.
Spread and Bake: Visually divide the prepared sheet pan into thirds. Spread each color of batter into a thin, even layer side by side, about 5 inches wide per section. Use an offset spatula to smooth the tops.
Bake for 23–25 minutes, or until set and lightly golden. Let cool completely.
Separate and Assemble the Layers: Once cooled, cut between the colors to separate the three cake layers. Place one layer flat-side up and spread a thin layer of jam on top. Stack the second layer on top and spread another thin layer of jam. Finish with the final layer, placing it flat-side up for an even top.
Press and Chill: Cover with parchment paper, then place another sheet pan on top. Weigh it down with cans or heavy items and refrigerate for at least 8 hours or overnight.
Melt and Spread the Chocolate: Melt the chocolate in a double boiler until smooth and glossy. Spread a thin, even layer over the top of the chilled cake using an offset spatula.
Refrigerate until set, about 15 minutes. Flip and repeat on the other side. Chill again until fully firm.
Trim and Cut: Trim the edges using a serrated knife. Cut into long strips, then slice into squares. For the cleanest cuts, run the knife under warm water and dry it between slices.