clues
preheat the oven to 350ºf. grease three 8-inch square pans and line them with parchment paper that comes at least 2 inches up two of the sides of the pan. if you don't have 3 pans, you can bake the layers in batches.
in a large bowl or in a stand mixer fitted with a whisk attachment, beat the egg whites to soft peaks. with the mixer running on medium, gradually add the 1/4 cup of sugar. increase the speed to medium-high and beat to stiff peaks. set them aside (see note). in a large bowl or in a stand mixer fitted with a paddle attachment, beat together the butter, almond paste, salt, and remaining 1 cup sugar on medium-high speed until light and fluffy, 2 to 3 minutes. reduce the speed to medium and add the yolks, one at a time, beating well after each. beat in the lemon juice and almond extract, then reduce the speed to medium-low and gradually add the flour. mix to combine. use a rubber spatula to fold in the whites.
transfer one-third of the mixture to one of the pans and use a small offset spatula to spread it out evenly. transfer another third of the mixture to a separate bowl and fold in the green food coloring. fold the red food coloring into the remaining third. transfer these into the remaining 2 pans, spreading them out evenly.
bake until the tops are just set and no longer shiny. begin checking for doneness at 15 minutes. let cool in the pans for 5 minutes and then lift them out and place on a wire rack to cool completely.
stack them up (from bottom to top: green, white, red) with 3 tablespoons jam between the layers. wrap the loaf firmly in plastic wrap and refrigerate for at least 4 hours or overnight.
with a long sharp knife, cut the cookie loaf into long skinny slices, 1/2" thick. line the bottom and two sides of a 9” x 13” pan (or something of relatively similar size, i used an 8” x 8” pan plus a loaf pan) with parchment paper, allowing parchment wings to come all the way up the sides. lay the cookie slices flat and snuggly in the bottom of the pan. soften 3 pints of gelato at room temperature for about 15 minutes, until spreadable. give the gelato a little stir so it’s all one consistency and then spread it evenly over the cookie slices. top with the remaining cookie slices and then freeze for 4 hours or overnight, until firm. use the parchment wings to lift your giant cookie sandwich out of the pan and onto a cutting board. with a sharp knife, trim the edges so they’re nice and even and then cut into squares. (save edge scraps in an empty talenti container!)
Note: with any recipe that calls for beating something else in the same mixer, I do a few steps to cut down on dishes and ensure that my egg whites don't have any bit of yolk in them, which will cause them not to beat to stiff peaks. I first separate an egg into 2 medium bowls. I then pour the white into my mixer bowl. then I repeat for each egg, adding the whites one by one so that if one gets contaminated, they're not all ruined. and then i beat the whites to stiff peaks first, scoop them out of the mixer bowl, and then use the mixer bowl for the next step. if you use a rubber spatula to get 95 percent of the whites out, there's really no need to rinse the mixer bowl for the yolk step.
