Cut the butter into 1- to 1 ½-inch pieces and place them in a small bowl. Freeze while you prep the rest of the ingredients.

In the bowl of a stand mixer fitted with the paddle attachment, combine the flour ½ cup of the sugar, and the salt. Beat on low until just combined, about 15 seconds. Add the butter all at once and beat on low until the dough starts to resemble coarse meal, with pea-sized pieces of butter throughout, about 3 minutes. Increase the mixer to medium and beat until the dough clumps around the paddle and/or the sides of the bowl, 2 to 3 minutes. If necessary, use a mixer cover or kitchen towel while beating to prevent any pieces of dough from shooting out of the bowl.

Tip the dough out onto a piece of parchment paper around the size of a half sheet pan and use your hands to shape it into a roughly 6-inch square. Place a second sheet of parchment paper over the dough, creating a parchment sandwich with the dough in the middle. Use a rolling pin to flatten the dough between the parchment sheets, working from left to right. Turn the dough 90 degrees and repeat every so often, doing so will prevent the dough from cracking as you roll it. If the parchment starts to wrinkle and leave creases in the dough, pull the sheet loose and smooth it before rolling the dough more. Continue rotating and rolling until you have a 9-inch square of dough around ¼ inch thick.

Remove the top layer of parchment. Press a bench scraper against the sides of the dough to create straight edges. Transfer the slab of cookie dough, still on the bottom layer of parchment, to a half sheet pan. Cover with the top layer of parchment once more and refrigerate for at least 2 hours, preferably overnight.

Position a rack in the center of the oven and preheat oven to 350 degrees F.

Remove the sheet pan of dough from the refrigerator. Use the overhanging parchment as handles to carefully lift the slab of dough off the sheet pan and onto a cutting board. Peel the top layer of parchment from the slab and use it to line the sheet pan once more. Line a second half sheet pan with parchment as well.

Use a paring knife to slice the slab of dough in half lengthwise, then slice each portion in half crosswise. You should have four smaller dough slabs of equal size. Repeat the process with each of the smaller dough slabs until you have sixteen 2-inch-square cookies. Place the cookies at least 2 inches apart on the prepared sheet pans. Sprinkle remaining 2 tablespoons of sugar evenly over each cookie. The dough should still be cool and firm to the touch. If not, chill both sheet pans in the freezer for at least 10 minutes before baking.

Bake one pan at a time (keeping the other pan in the refrigerator) for 15 to 17 minutes, or until the edges of each cookie are pale golden brown with small hairline cracks visible on their surfaces. For straight cookie edges, gently press a bench scraper against the side of each cookie immediately after removing the cookies from the oven. Cool the cookies on the pan on a wire rack for 20 minutes, or until the edges an bottoms of the cookies are set and feel firm to the touch. Repeat to bake the remaining cookies. Serve warm or at room temperature.