I never did get around to making these cookies, but as mentioned in this Instagram feed, I do have the proper ingredients. Since they aren’t necessarily a Christmas cookie, I don’t have to wait until next December. In fact, maybe I’ll try them for Independence Day and make US Flag cookies, instead of Italian ones!

Seven Layer Cookies from Smitten Kitchen

And here’s a cute picture showing one of the other types of Christmas treats they made!

Updated April 2019:
I didn’t make them for Independence Day last year, but I did make them for Easter this year! Just in case the linked recipe disappears, here’s what I did, using a brand-new ingredient (at least to me), almond paste.
Venetian Squares
4 eggs, separated
1 cup sugar, divided
1 package almond paste (mine was 8 oz; Elizabeth’s was 7 oz)
1 1/4 cups butter (2 1/2 cubes)
1 teaspoon almond extract
2 cups flour
1/4 teaspoon salt
red and green food coloring
3 1/2 ounces seedless raspberry jam (Note that this is half of what the original recipe called for, but even this was almost too much for my tastes.)
1 1/3 cups semi-sweet chocolate chips (Note that we wouldn’t have minded having a thicker layer of chocolate!)
Beat the egg whites for a few minutes, then gradually add 1/4 cup sugar and beat until very stiff; set aside. Cream together the remaining 3/4 cup sugar and the almond paste. Note that this was a spattery mess, and the two never did really incorporate; use a large bowl. Add the butter and cream again. Stir in the egg yolks and almond extract and beat until smooth. Carefully mix in the flour and salt, then gently fold in the egg whites. Divide the dough evenly into three smaller bowls. Add a few drops of red food coloring to one bowl, green to another, and leave the third plain.
Preheat oven to 350 degrees. Mark a 9 x 12 inch rectangle on a sheet of parchment paper, then place it on a cookie sheet. Carefully spread the red dough on the parchment paper, then bake for 8-10 minutes. When done, move to a cooling rack, using the parchment paper to lift it. Repeat for the other two colors.
When all the layers are cooled, line a cookie sheet with some wax paper and place the green layer on top. Heat your jam until it’s melted (strain if you can’t find seedless jam) and spread half of it over the cake. Top with the white layer and repeat. Place the red layer on top, cover with plastic wrap, top with a baking pan filled with weights (I used cans), and place in the refrigerator for several hours.
For the final step, remove the dessert. Melt half the chocolate (1 minute at 50% power in the microwave works for me) and spread over the red layer. Return to the refrigerator for 15 minutes to harden. Flip the dessert onto another wax-paper-lined cookie sheet, melt the remaining chocolate, and spread it over the green layer. Chill until firm.
Carefully slice into squares using a serrated bread knife. I cut ours into 60 pieces, which equals 115 calories each.