3 quarter-sheet pans or three 13-by-9-by-2-inch jelly roll pans
Preheat the oven to 350 degrees F. Coat 3 quarter-sheet pans (or three 13-by-9-by-2-inch jelly roll pans) with cooking spray. Line each pan with parchment paper and coat the paper with cooking spray as well.
Place the almond paste in the bowl of a stand mixer. Break it up into small pieces with a fork. Fit the mixer with the paddle attachment and add the butter and sugar to the bowl. Beat the mixture on high speed until light and fluffy, about 7 minutes. Reduce the speed to medium, add the egg yolks, and beat until incorporated. Turn the mixer off and stir in the flour with a wooden spoon until well combined. Transfer the mixture to a medium bowl.
Clean the mixer bowl thoroughly and fit the mixer with the whisk attachment. Beat the egg whites on high speed until stiff peaks form. Fold the egg whites into the batter until thoroughly blended.
Transfer 1 1/2 cups of the batter to a medium bowl, then transfer another 1 1/2 cups of the batter to a second medium bowl. Add the red food coloring to one of the bowls and stir until the batter is tinted throughout. Add the green food coloring to the second bowl and stir until the batter is tinted throughout. Scrape each of the three batters into one of the prepared pans, using the spatula to spread the batter to the edges. Bake, rotating and switching the positions of the pans halfway through, until the edges are golden, 12 to 14 minutes. Let cool in the pans for about 5 minutes, then invert onto cooling racks and allow to cool completely.
To assemble, place the green layer on a large cutting board or a large inverted baking sheet lined with wax paper. Spread the raspberry jam evenly over the top. Place the yellow layer on top and spread with the apricot preserves. If there are large chunks of apricots, remove and chop them up to make them more spreadable. Top with the red layer. Cover with plastic wrap and place a heavy cutting board on top to weight it down. Refrigerate overnight.
Place the chocolate chips in a microwaveable bowl and melt in the microwave on low power about 2 minutes. Spread the chocolate on top of the cooled cake and let dry slightly. Trim the rim of the cake with a serrated knife to make clean edges. Cut the cake crosswise into twelve 1-inch-wide strips, then cut lengthwise into 1 1/4-inch strips. The cookies will keep, covered, up to 1 week.