2 cups sliced almonds, preferably unblanched
1 cup plus 2 tbsp powdered sugar
16 tbsp unsalted butter, softened (2 sticks)
1/2 large egg, lightly beaten
1 tsp vanilla extract
1 3/4 cups plus 1 tbsp bleached all-purpose flour
1/4 tsp fine sea salt
2 2/3 cups dried apricots (1 lb)
1 cup plus 2 tbsp granulated sugar
2 tsp lemon zest, finely grated
1 tsp apricot or peach brandy
8 oz bittersweet chocolate, chopped
1/4 cup heavy cream, hot
Grate almonds using nut grater.
In the bowl of a stand mixer fitted with flat beater, beat almonds, powdered sugar, and butter until fluffy. Scrape down sides of bowl. Add egg and vanilla; beat until blended.
Whisk together flour and salt. On low speed, gradually add flour mixture to butter mixture. Mix until incorporated and dough begins to come away from sides of bowl.
Scrape mixture into a plastic bag and press it together. Remove dough from bag and transfer to a large sheet of plastic wrap. Use the edges of the wrap to knead dough until smooth.
Divide dough into quarters. Wrap with plastic and flatten into disks. Place in freezer bag. Refrigerate for at least 2 hours and up to 2 days.
In a medium saucepan with a tight-fitting lid, soak dried apricots in 2 cups water for 2 hours. Bring to a boil, cover, and simmer for 20-30 minutes on the lowest heat until apricots are very soft. If water evaporates, add a little extra.
In a food processor, pulse apricots and liquid with sugar, lemon zest, and brandy.
Return mixture to saucepan and simmer, stirring, 10-15 minutes, until deep orange and thick.
Transfer to a bowl; let cool. (You will need only about 2/3 cup, but the leftover will keep almost indefinitely when refrigerated.)
Preheat oven to 350°.
Set 1 dough disk on a lightly floured surface. Lightly flour dough and re-cover it with plastic wrap. Let dough soften until malleable, about 10 minutes. Roll 1/8" thick, adding more flour if necessary to keep dough from sticking.
Cut out 20 cookies. Place 1/2" apart on a parchment-lined baking sheet. (Set aside scraps; cover with plastic wrap.) Bake cookies 4 minutes. Rotate the cookie sheet then continue baking for 2-6 minutes, or until edges brown.
Let cookies cool on a wire rack.
Repeat process with remaining dough disks. (After the last batch is cut, you can knead together all the scraps and repeat chilling, rerolling, and cutting.)
Heat chocolate in a bowl set over hot water (not touching), stirring with a silicone spatula, until almost completely melted. Remove from heat and stir until fully melted.
Add cream; stir until smooth. (The mixture should drop thickly from the spatula. If the ganache thickens before it’s used, reheat in the microwave in 3-second bursts.) Set aside.
Spread bottoms of half of the cookies with a thin layer of apricot filling. Spread bottoms of the remaining cookies with a slightly thicker ganache layer. Set the chocolate cookies, coated side down, on the apricot cookies. Let sit for a minimum of 30 minutes.
Store airtight at room temperature, 5 days; frozen, 6 months.