Italian Rainbow Cookies

8 ounces almond paste
1 cup granulated sugar
2 + ½ sticks (1 + ¼ cups) unsalted butter, softened, cut into pieces, plus more for the pans
4 large eggs, separated
½ teaspoon salt
2 cups all-purpose flour, sifted (measure first), plus more for the pans
1 teaspoon red food coloring, gel or paste preferred
1 teaspoon green food coloring, gel or paste preferred
2 (15-ounce jars) smooth apricot or seedless raspberry jam
1 pound semi-sweet or bittersweet chocolate, chopped small
1 teaspoon melted shortening

Preheat the oven to 350 degrees F. Butter and flour three 15-by-10-inch rimmed sheet pans and line the bottoms of the pans with parchment paper.
Mix the almond paste and all but 2 tablespoons of the sugar in an electric mixer fitted with the paddle attachment on medium speed until you have fine crumbles.
On low speed add the butter, a little at a time and mix until well combined.
On low speed add the egg yolks, one at a time, and mix until smooth.
Beat in salt and flour on low speed until just combined.
In a separate bowl beat the egg whites until foamy while slowly adding the remaining 2 tablespoons sugar, continue beating on medium speed until stiff peaks form. When the beater is lifted the whites should stay stuck to it.
Fold about a third of the egg whites into the batter to start then gently fold in the remaining egg whites.
Divide the batter evenly into three bowls. Leave one bowl plain. Add red food coloring to the second stirring to make a deep-salmon color. Add green food coloring to the last bowl, stirring to make a medium-green color.
Spread batter into each of the prepared pans with an offset spatula as evenly as you can - it will be very thin.
Bake, rotating pans to opposite racks, until cakes are cooked through and just beginning to brown around the edges, about 8 to 10 minutes.
Remove from oven and let cakes cook completely on wire racks.
Put the green cake on a large cutting board and spread one jar of jam evenly over the cake almost to the edges. Top with the plain layer.
Spread the remaining jar of jam over the plain layer almost to the edges. Top with the red layer.
Top the red layer with a piece of parchment then wrap the entire cake in plastic. Top with another pan, weighted with cans.
Chill in a cool place or in the refrigerator at least 4 hours or overnight.
Unwrap the cake. Melt the chocolate in a double boiler or using the chocolate setting on your microwave until smooth. Stir in the shortening.
Pour the chocolate over the top the cake and spread it evenly from edge to edge with an offset spatula. Allow the chocolate to set in a cool place or in the refrigerator. If you like you can run a fork through the chocolate when it is halfway set from one end to the other, slightly undulating it so it looks like waves, repeating until it is entirely striped.
Use a serrated knife to cut into rows then cut the rows into squares or rectangles. Wipe the knife clean with a wet cloth after each cut.
Store in a tightly covered container in a cool, dry place or in the refrigerator up to 1 week.