Preheat oven for 325˚F. Grease three separate 9x13-inch quarter sheet baking pans or cake pans with cooking spray. Line each with parchment paper, letting it hangover the sides for easy removal.
Add sugar, almond paste, and 8 Tbsp (1 stick) unsalted butter to a stand mixer fitted with a paddle attachment. Beat until smooth and there are no more lumps. Beat in remaining butter until smooth, scraping down the sides as needed with a spatula.
Add the egg yolks in, beating until combined. Beat in milk and almond extract until combined. Add flour, slowly mixing in until combined, scraping down the sides of the bowl as needed. Once combined, set aside.
Add egg whites to a large bowl, beating with a handheld electric mixer until they form still peaks. Fold the egg whites into the almond flour mixture to form the batter until combined. Divide the batter equally into three separate bowls.
Stir in red food coloring into the first bowl until evenly colored. Stir in green food coloring into the second bowl until evenly green in color. Leave the third bowl untouched.
Evenly spread each batter into its own greased and parchment-lined pan. Bake, rotating halfway through, until set, about 10 to 12 minutes. Cool completely in the pans.
Once cooled, remove the green cake from the pan onto a large sheet pan, removing the parchment paper from the bottom. Spread half the jam on top of the green cake. Remove the parchment off the undyed layer and place on top. Spread with remaining jam and top with the pink layer, making sure to remove the parchment paper before.
Cover the layered cakes with plastic wrap and top with another sheet pan. Weight the layers down using heavy plates and refrigerate for 4 hours or overnight.
Remove weights and plastic wrap, then spread half the melted chocolate on top of the cake. Place in the refrigerator to set for 30 minutes. Once solid, carefully flip cake onto a cutting board. Spread with remaining chocolate in an even layer. Return to the refrigerator to let set for 30 minutes.
Once set, trim edges to make even. Then cut into 1 1/2 inch squares. Serve.