Make the cookie dough: In a bowl, beat 1⁄2 cup flour, butter, and confectioners' sugar with a handheld mixer on medium speed until pale and fluffy, 1–2 minutes. Add yolks one at a time, beating until smooth after each addition. Add salt and remaining flour; beat to make a dough. Halve dough, flatten into 2 disks, and wrap each with plastic wrap. Refrigerate dough for 1 hour.
Make the filling: Heat oven to 325°. In the bowl of a food processor, process the pistachios with the sugar until finely ground. Add almond paste and process until combined. Add the kirsch and vanilla and process until combined; set filling aside.
Transfer one dough disk to a lightly floured surface and roll with a floured rolling pin to a 1⁄8" thickness. Using a 3⁄4" round cookie cutter, cut out 24 cookies. Repeat with remaining dough. (Combine and re-roll scraps to make 48 cookies in all.) Place cookies 1" apart on two parchment paper–lined baking sheets and bake, rotating pans halfway through, until cookies are pale golden, about 20 minutes. Let cool.
Meanwhile, make the glaze: Bring sugar, corn syrup, and 3 tbsp. water to a boil in a 1-qt. saucepan over high heat. Remove from the heat, add chocolate, and swirl pan to coat the chocolate with the sugar mixture. Let sit without stirring to allow the chocolate to melt, about 5 minutes. Slowly stir the chocolate with a rubber spatula until smooth; set aside to let cool slightly.
Spoon about 1 tsp. of the filling onto 24 cookies and top with remaining cookies. Gently press cookies together to sandwich them. Dip half of each cookie into the chocolate glaze. Transfer to a rack and let the glaze solidify.