Before beginning, place an oven rack in the middle position. Preheat oven to 350°F (177°C). Make a parchment paper sling to line a 9X13-inch baking pan. Be sure to crease and fold in the corners. I use small metal binder clips to hold the sling in place.
In a mixing bowl, whisk together the flour (2 cups) and baking powder (1/2 teaspoon); set aside.
In a food processor, process granulated sugar (1 ½ cups) and almond paste (8 ounces) until combined, 20 to30 seconds
Transfer the almond paste mixture to the bowl of a stand-up mixer. Add eggs (7), vanilla (1 teaspoon), and salt (1/2 teaspoon).
Attach the whisk attachment to the mixer and set the mixer to medium-high speed and whip until the mixture is pale and thick about 5-7 minutes. Turn the mixer to low speed and pour in melted butter (8 tablespoons).
Gradually add the flour mixture to the mixer, and beat on low just until combined.
Pour 2 cups (measure-do not approximate) of batter into the prepared parchment-lined baking dish. Smooth out the top of the batter with an offset spatula.
Bake 11-14 minutes, or until the edges are just beginning to become golden and the center is set (touch center, if it leaves an indentation, the batter is not done.) My layers were baked for 12-13 minutes.
Allow the layer to cool in the pan for 7 minutes. Remove the layer from the baking pan, and continue to cool on a wire rack. Allow the baking pan to cool. Allow the cake layer to cool completely,
Divide the remaining batter between 2 bowls. Add the remaining batter between 2 small mixing bowls. Stir red food coloring (1/4 teaspoon) into one bowl then green food coloring (1/4 teaspoon) into the other bowl.
Make a new parchment sling for the now-empty and cooled baking pan and repeat baking with each colored batter. Allow the baking pan to cool after each batch.