Position oven racks in the upper third and lower third of the oven. Preheat the oven to 325°F. Lightly grease 3 (9×13-inch) baking pans or quarter sheet pans and line with parchment paper.
In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat together 1/2 cup of butter, the sugar, and almond paste on medium speed until smooth, - about 1 minute. Add the remaining 1 cup of butter. Beat on medium until light and fluffy, about 2 to 3 minutes.
With the mixer on low, add the egg yolks and almond extract, beating until just combined. Gradually add flour and salt, beating until just combined. Stop occasionally and scrape - down the bowl during mixing.
In a large mixing bowl, beat the egg whites with an electric mixer with clean beaters or the whisk attachment on high speed until stiff peaks form, about 5 minutes. Working in - batches, gently fold the egg whites into the cookie batter until combined and no streaks of egg white remain. Divide the batter evenly among 3 bowls.
Stir about 8 drops of red food coloring into one of the bowls of batter until fully combined. Spread into an even layer in 1 prepared pan. To another batter bowl, stir in about 8 - drops of green food coloring and spread into another prepared pan. Spread the remaining plain batter into the remaining prepared pan.
Place 2 pans on the upper third rack, ensuring the pans are not touching, and 1 pan on the lower third oven rack.
Bake for 15 minutes, then rotate the pans on the top rack to the bottom rack and vice versa. Continue baking until a wooden pick inserted in the centers of each cookie pan comes - out clean, about 12 minutes more. Let the cookies cool completely in the pans on wire racks.
With the cooled green layer still in the pan, spread 1/4 cup of the jam in an even thin layer over the top. Flip the plain (un-dyed) layer on top of the jammy green layer and - carefully remove and discard the parchment from the plain layer. Spread the remaining 1/4 cup jam in an even thin layer over the plain layer. Place the red layer on top of the jammy - plain layer and remove and discard the parchment. Cover with a sheet of plastic wrap.
Place one of the baking pans on top of the stacked layers. Evenly place weights (such as plates or canned vegetables) on top of the pan. Refrigerate for at least 4 hours or up to - 12 hours.
Once chilled, remove the weights and plastic wrap. Place a large cutting board on top of the stack and invert. Carefully remove and discard the parchment paper from the green - layer. Using a serrated knife, trim the edges to straighten. Place the stack, green layer up, on a wire rack set inside a large, rimmed baking sheet.
In a medium, microwave-safe bowl, heat half of the chocolate chips in 30-second intervals stirring between each, until the chocolate is melted. Spread the melted chocolate over the bottom stack. Let cool slightly, about 5 minutes.
Refrigerate, uncovered, until the chocolate is set, about 30 minutes.
In a medium, microwave-safe bowl, heat the remaining chocolate chips in 30-second intervals stirring between each, until the chocolate is melted. Spread the melted chocolate over the top and sides of the stack. Let cool slightly, about 5 minutes.
Using fork tines, scrape wavy lines into the chocolate. Refrigerate, uncovered, until the chocolate is set, about 30 minutes.
Using a serrated knife, slice the slab into 2-inch squares. Store the cookies in an airtight container at room temperature for up to 1 week or refrigerated for up to 2 weeks.