In a medium bowl, whisk together the cornstarch, flour, baking powder, baking soda, and salt.
Set aside. In the bowl of a stand mixer fitted with a paddle attachment, cream together the butter and sugar on medium speed until the mixture is light in color and fluffy, about 3 minutes.
Add the egg yolks, pisco or brandy, and vanilla and mix until incorporated, about 30 seconds.
Stop the mixer and scrape down the sides of the bowl with a rubber spatula.
With the mixer on low speed, gradually add the flour mixture and mix until just incorporated with no visible white pockets of flour, about 30 seconds.
Turn the dough out onto a piece of plastic wrap, shape it into a smooth disk, and wrap it tightly.
Place in the refrigerator until firm, at least 1 hour or overnight.
Preheat the oven to 350°F and place rack in the middle position. Line two baking sheets with parchment paper and set aside.
Remove the dough from the refrigerator, unwrap it, and place it on a lightly floured work surface.
Lightly flour the top of the dough.
With a rolling pin, roll the dough out to ¼-inch thickness (the dough will crack but can be easily patched back together).
With a 2-inch round or fluted cookie cutter, cut out 24 rounds of dough, rerolling the dough as necessary until all of it is used up. Place the cookies on the prepared baking sheets, 12 per sheet and at least ½ inch apart.
Bake 1 sheet at a time until the cookies are firm and pale golden on the bottom, about 12 to 14 minutes. (The cookies will remain pale on top)
Transfer to a wire rack to cool completely.
Carefully flip half of the cookies upside down (these cookies are very delicate and may break easily, so use care) and very gently spread a thick layer of dulce de leche, about 2 teaspoons, on the upside down cookies.
Place a second cookie on top and gently press to create a sandwich.
Dust generously with powdered sugar before serving.