Position two racks in the upper and lower thirds of the oven and preheat to 350 (F). Lightly coat three 8-inch square pans (see baker’s notes) with cooking spray and line with parchment paper, leaving an overhang on two opposite sides of the pan. Spray the parchment paper, too.

Divide the batter evenly among three bowls, using a digital scale to weigh out around 9 ounces of batter per bowl. Use a rubber spatula to mix the almond extract into the first bowl of batter and pour into the prepared cake pan, using an offset spatula to spread the batter evenly across the pan and smooth the top. Mix the lemon extract and yellow food coloring into the second bowl of batter and pour into a second cake pan, using an offset spatula to spread the batter evenly across the pan and smooth the top. Mix the orange blossom water and orange food coloring into the last bowl of batter and pour into the final cake pan, using an offset spatula to spread the batter evenly across the pan and smooth the top.

Place two cake pans on the upper third rack of the oven and the third cake pan on the lower third rack. Bake for 12 to 15 minutes, rotating the pans on the upper third rack to the bottom third rack and vice versa, about halfway through the baking time. The cakes are done when a skewer inserted into the center of each comes out with few crumbs attached and the top of each cake springs back when gently pressed. Cool the cakes completely in their pans on a wire rack.

Remove the white cake from its pan by turning it upside down onto a chopping board. Peel off and discard the parchment paper. Use an offset spatula to spread half of the jam evenly over the top. Remove the orange cake from its pan by turning it upside down onto a chopping board. Peel off and discard the parchment paper. Carefully layer the orange cake on top of the jam-covered white cake. Use an offset spatula to spread the remaining half of the jam evenly over the top. Remove the yellow cake from its pan by turning it upside down onto a chopping board. Peel off and discard the parchment paper. Carefully layer the yellow cake on top of the jam-covered orange cake. Press down on top of the yellow cake to adhere the layers and wrap tightly in plastic wrap; chill for at least 1 hour.

To make the cookies, trim about ½ inch on each side of the square. Use a serrated knife to cut the cake crosswise into 1 ½-inch-wide strips. Cut the strips crosswise into ¾-inch-thick pieces.