Prepare the sheet pans. Position a rack in the middle of the oven and preheat to 350 F. Grease, flour, and line the bottoms of three 9- by 13- by 2-inch (quarter sheet pan) with parchment paper, leaving a 2-inch overhang.
Beat egg whites. In the bowl of a standard electric mixer fitted with the whisk attachment, beat egg whites at medium-high speed until they just hold stiff peaks. With the mixer running on high speed, add ¼ cup sugar a little at a time, beating until whites hold stiff, glossy peaks. Transfer to another bowl, and wipe the bowl dry with a paper towel.
Mix sugar and almond paste. Switch the mixer to the paddle attachment and beat together the almond paste and remaining ¾ cup sugar until well-mixed, about 3 minutes.
Incorporate butter. Add butter and beat until pale and fluffy, about 3 minutes. Add yolks and almond extract and beat until well combined, about 2 minutes. Reduce speed to low, then add flour and salt, mixing until just combined.
Fold in egg whites. Fold half of egg white mixture into almond mixture to lighten, then fold in remaining whites gently but thoroughly.
Divide batter among 3 bowls. Stir red food coloring into one bowl and green food coloring into another, leaving the third bowl plain. Keep in mind the batter will bake up darker than it looks pre-bake. Pour the batter from one of the bowls into one of the prepared pans. (I only have one sheet pan of this size, so I just bake each layer off one at a time.) Using an offset spatula, spread the batter into an even layer.
Bake the individual layers. Bake the layer for 8 to 10 minutes, until just set (the cake may look undercooked, but this is what you want). Repeat with the remaining bowls of cake batter and sheet pans, transferring each baked cake to a wire rack to cool completely.
Assemble the layers with preserves. When all the layers are cool, invert the green layer onto a parchment- or wax paper-lined baking sheet. Peel off the paper from the layer and brush on half of the heated preserves. Flip the white layer on top of the green layer and peel off the paper. Spread with remaining preserves. Invert the red layer on top of white layer and discard the paper.
Chill overnight. Cover tightly with plastic wrap and place another quarter sheet pan on top, right side up. Evenly distribute a heavy weight on top of the sheet pan — I place heavy cookbooks on top! — and place in the fridge to chill for at least 8 hours or overnight.
Bring the cake to room temperature. Remove the weights and plastic wrap and let the layer sit on your counter for a few minutes to come to room temperature. Melt the chocolate wafers in a microwave-safe bowl in 30-second increments, until smooth.
Pour on melted chocolate. Trim the edges of the assembled layers with a long serrated knife to even them out. Quickly (like REALLY quickly) spread half of the melted chocolate in a thin layer on top of the cake. Place the cake back in the fridge to firm up the chocolate, about 10 to 15 minutes. Place a sheet of wax paper on top of the chocolate layer, place another quarter sheet pan on top, then invert the cake and remove the paper. Quickly spread with the remaining chocolate. Freeze the chocolate-covered cake until just slightly firm, about 10-15 minutes.
Slice cookies. Cut lengthwise into 6 strips, then cut each strip crosswise into 16 pieces. It helps to use a sharp serrated knife that has been run under hot water to cut into the frozen cake. The cookies are much easier to cut when cold!
The cookies can be stored in an airtight container in the fridge or freezer.