Preheat oven to 350 F. Spray three rimmed quarter sheet baking pans (9×13 sheet pans) with cooking spray and then line with parchment paper.
Using a stand mixer or hand mixer, cream the almond paste with ¾ cup sugar on low speed until well combined, about 2-3 minutes. Add butter and beat on medium speed until light and fluffy, about 2 minutes.
Add in egg yolks, almond extract, and salt and continue to beat until incorporated.
Reduce the mixer speed to low and add the flour. Mix until just combined.
In another mixing bowl, whip the egg whites at medium-high speed until they just hold stiff peaks. Then add the remaining ¼ cup sugar and beat on high speed until they form stiff, glossy peaks, about 2-3 minutes.
Fold the egg whites into the batter. Divide the batter evenly into 3 mixing bowls. You can use a kitchen scale to accurately divide the batter into thirds.
Stir in a few drops of red food coloring into one bowl and a few drops of green food coloring into another, leaving the last bowl plain. Note that the batter will bake up darker than it looks when raw.
Pour the batter from each of the bowls into a separate prepared pan. Use a small icing spatula to spread the batter into an even thin layer.
Bake each layer for 8-10 minutes, until the edges just start to brown. Allow the cakes to cook in the pan for 10 minutes, then carefully transfer to a wire cooling rack to cool completely.