Step 1

For the almond sponge cake: Preheat the oven to 350 degrees F. Butter the bottoms and sides of three 13-by-9-inch baking pans. Line the bottoms and sides of the pans with parchment paper and grease the paper with additional butter.

Step 2

Combine the butter, almond paste, sugar, orange zest and vanilla seeds in the bowl of a stand mixer. Using the paddle attachment, beat until all ingredients are fully combined and the mixture is light and fluffy, about 5 minutes. Add half of the egg yolks, and mix until they are fully incorporated. Repeat with the remaining egg yolks. Add the flour in 1 addition and, with the mixer on low speed, beat just until combined.

Step 3

In a separate bowl with clean beaters, whip the egg whites with the salt to stiff peaks and add them to the bowl with the batter. Fold the whites into the batter by hand; the finished batter will be thick.

Step 4

Divide the batter evenly into 3 bowls, using about 1 1/2 cups of batter per bowl. Add the red food coloring to one bowl, and the green to another. Leave the third bowl as is. Fold the food coloring into the batter, being sure to rinse your spatula or spoon before switching colors. Transfer each batter to its own baking pan. Use an offset spatula to spread the batter evenly in the pans. Bake the cakes until the sides begin to pull away from the pan, 10 to 12 minutes. Remove the cakes from the pans right-side-up and allow them to cool completely on cooling racks.

Step 5

To begin assembly, carefully flip the red cake onto a plastic cutting board. Apply a thin layer of the cherry preserves on top. Flip the uncolored cake onto the red layer. Spread a thin layer of apricot jam onto it. Flip the green cake onto the uncolored layer. Cover the entire cutting board with plastic wrap, transfer it to the refrigerator and place a heavy book on top of it; chill overnight.

Step 6

For the chocolate glaze: Put the chopped chocolate and honey in a heat-resistant bowl. Bring the heavy cream to a simmer in a small saucepan and pour over the chocolate. Allow the mixture to sit for a minute, then whisk until all the chocolate is melted. Add the butter and whisk until it is completely melted and all ingredients are fully combined.

Step 7

Remove the cake from the refrigerator and cut it into 1 1/2-inch-wide strips. Transfer the strips to a wire rack, making sure to keep space between the strips. (You may need to use 2 racks, or glaze the cakes in 2 batches.) Place the rack over a piece of plastic wrap to catch excess glaze. Spoon the glaze over the cake strips, allowing it to drizzle down the sides. Use an offset spatula to smooth the tops. Working one strip at a time, cut the strips into 3/4-inch pieces, wiping your knife often to keep it clean. Allow the glaze to set completely before transferring the cookies to an airtight container. The rainbow cookies will keep for 3 days at room temperature or up to a week refrigerated.