In a food processor, break up almond paste, butter, sugar, egg yolks, and almond extract. Beat 5 minutes or until smooth. Place into a large bowl, stir in flour with whisk. Set aside.
In a dry glass bowl, whip egg whites and vanilla until stiff peaks form. Fold egg whites into almond mixture until incorporated. Do not overmix!
Get two more bowls and divide batter into three equal parts. Add green food coloring to one bowl, red food coloring to another, and leave the last alone. Gently mix in the coloring.
Preheat oven to 350°F. Line 3 9x13x2" tins with parchment paper. Spread batter into pans. Bake 13-14 minutes. Let cool 10 minutes.
Spread jam on the green layer, place the white cake on top and then spread jam on the white layer and place the red layer on top. Leave the stacked cakes in the first pan, cover with wax paper, then aluminum foil, and put in the refrigerator with something heavy on top to press down (like a large book).
The next day, melt the chocolate and spread over top of cake. Let cool, then cut into rectangles the size of your choosing. Keep refrigerated and enjoy!