Italian Rainbow Cookies are always a welcomed pop of color (and almond flavor!) on any holiday cookie tray!
Preheat the oven to 325°F (165°C). Butter and line three 9x13-inch (23x33-cm) quarter-sheet pans with parchment. Set aside.
In the bowl of a stand mixer fitted with a whisk attachment or with a handheld electric mixer and a medium bowl, whip the 4 egg whites on high speed to stiff peaks, for 3 to 5 minutes. Transfer to a separate bowl and set aside.
If using a stand mixer, switch to a paddle attachment (or continue to use the handheld electric mixer) and beat the butter and granulated sugar on medium-high until pale and fluffy, about 3 minutes.
Lower the speed to medium-low and beat in the almond flour and powdered sugar, followed by the egg yolks, milk, remaining egg white, and almond extract.
Fold in the flour until evenly combined, then gently fold in the reserved whipped egg whites until blended.
Divide the batter evenly among three bowls. In the first bowl, stir in the red food coloring. Stir the green food coloring into the second bowl and leave the last one uncolored.
Spread the batters into the prepared sheet pans and bake for 10-12 minutes, rotating halfway through, until slightly firm to the touch but still pale. Let cool completely.
Leave the green layer on the sheet pan and spread half of the jam evenly over the surface. Place the white layer on top and spread with the remaining jam. Top with the pink layer.
Cover with plastic wrap, then place a baking sheet on top of the stack and add some weights. (You can use cans, a book, or anything heavy.) Refrigerate like this for at least 4 hours or overnight.
Gently melt the chocolate and oil in a double boiler, stirring frequently, until smooth.
Spread half of the melted chocolate over the surface of the cake and refrigerate until the chocolate is set, about 30 minutes.