Step 1

Preheat the oven to 325° and grease three 9-by-13-inch quarter sheet pans with cooking spray, then line each with parchment. In a stand mixer fitted with the paddle attachment, combine the sugar, almond paste and 1 stick of the butter. Mix until smooth and lump free, being sure to break down the almond paste as best you can. Add the remaining 2 sticks of butter and continue to mix until smooth, scraping down the sides of the bowl as needed.

Step 2

Gradually add the egg yolks, followed by the milk and almond extract. Mix until combined. Add the flour and slowly mix until combined, scraping down the sides of the bowl as needed. Once the flour is combined, set aside.

Step 3

In a separate bowl, whip the egg whites until they form stiff, fluffy peaks. Fold the whipped egg whites into the flour mixture to form a smooth batter, then divide equally between 3 bowls.

Step 4

Stir the red food coloring into the first bowl of batter until evenly pink colored, then stir the green color into the second bowl of batter until evenly green colored, leaving the third bowl untouched. Keeping the batters separate, evenly spread them into the greased and parchment-lined quarter sheet pans, and bake, rotating halfway through, until set, 10 to 12 minutes. Then let cool completely.

Step 5

Once cooled, spread half of the jam to cover the surface of the green cake and place the undyed layer, making sure the parchment is discarded, directly on top, sandwiching the jam. Repeat this step by spreading the remaining jam on top of the undyed layer and placing the pink layer directly on top of it, discarding the parchment.

Step 6

Cover the cake with plastic wrap and top with another sheet pan. Weigh down the layers with heavy plates or cans, and refrigerate for at least 4 hours, or overnight.

Step 7

Remove the weights and plastic wrap. Spread half of the melted chocolate over the top of the cake and refrigerate until set, 30 minutes. Once solid, flip the cake onto a cutting board, discarding the bottom layer of parchment, and spread the remaining melted chocolate in a even layer over the surface. Return to the refrigerator and chill until set, 30 minutes.

Step 8

Once set, trim the cake into a 7½-by-10½-inch rectangle, reserving all trim for snacking or rainbow cookie ice cream (see the recipe). Cut the cake into 1½-inch squares, then serve.