Using a stand mixer with the paddle beater or electric mixer, combine cheese, butter, 1 teaspoon of salt, and pepper until it starts to stick to the sides of the bowl, about 1 minute.
Add flour and cornstarch and mix until combined, about 1 minute.
Add 2 tablespoons of water and mix briefly until dough ball forms. Add another tablespoon of water, if needed.
Transfer dough to floured counter and flatten into a disc. Wrap in plastic and refrigerate until chilled, about 30 minutes.
Adjust oven racks to upper-middle and lower-middle positions and preheat oven to 375°F/190°C. Line 2 rimmed baking sheets with parchment paper. Unwrap the dough and place on a floured surface. Roll to 1/16 inch thickness.
Cut into 1-inch squares using a beveled-edge ravioli cutter or pizza cutter. Transfer to baking sheets. Use a fork to make crimp marks on edges, if desired. Use the blunt end of a skewer to poke a hole in the center of each square. Sprinkle with remaining 1/2 teaspoon of salt.
Bake until light golden around the edges, about 18 minutes, switching racks and rotating sheets halfway through baking. Let cool completely on baking sheets.
Store in airtight container at room temperature for up to 3 days.