Pretzel Shortbread Cookies

1 large handful (about 12) thin hard pretzels
8 ounces unsalted butter, softened and cut into chunks
1 cup powdered sugar
1 1/2 cups all-purpose flour, plus more for sprinkling
1/4 cup food-grade lye (see note)
Pretzel salt, to top

INSTRUCTIONS

In the bowl of a food processor, pulse the pretzels to make pretzel flour until the pretzels are sandy in texture. Add the butter and powdered sugar to the food processor and process again until creamy and smooth. Add the all-purpose flour. Process again, stopping to scrape down the sides occasionally, if necessary, until a smooth dough forms.

Sprinkle a flat countertop with additional flour to prevent sticking. Shape the dough into a ball, then drop against the counter on alternating sides to flatten and use your hands to create a brick-like shape. Try to make sure that there are not many cracks in the dough but be careful not to overwork. Wrap and refrigerate the dough until firm, about 1 hour.
Cut the uneven sides off of the dough and slice into 1/2″ thick squares. (If the dough crumbles, leave at room temperature 5 to 10 minutes). Place the slices on a parchment or wax paper lined baking sheet and freeze until firm, at least 1 hour.
Preheat the oven to 350°F.
While wearing gloves, carefully combine 5 cups cold water and 4 tablespoons food-grade lye in a nonreactive bowl in a well-ventilated area. Whisk until lye fully disintegrates. Dip the shortbread, one at a time, in the lye mixture for 15 seconds, then transfer briefly to a rack set over a baking sheet to drip off excess liquid.
Place the shortbread on an ungreased baking sheet (not nonstick!) and gently pierce with a fork. Sprinkle generously with pretzel salt. Make sure to work quickly so that the shortbread stays cold.
Bake until golden brown and still slightly soft to the touch, about 20-25 minutes, rotating halfway through.
Allow to cool and harden on the baking sheet, then remove with a spatula before serving or wrapping.