Process the shredded cheddar cheese, flour, cornstarch, and salt together in a food processor until combined, for about 30 seconds. Add the butter and process until mixture resembles wet sand, for about 20 seconds. Add the water and pulse until dough forms large clumps, about 10 pulses.

Transfer the dough to a lightly floured work surface. Divide it in half and pat each portion into a 6-inch square. If the dough feels dry, moisten your fingers with cold water as you smooth out the dough. Carefully wrap each square in plastic wrap and refrigerate until firm, about 45 minutes and up to 2 days.

Preheat oven to 350°F. Line 2 large baking sheets with parchment paper or silicone baking mats.

Unwrap each dough square. Place each on a lightly floured work surface and roll out into a larger 9-inch square of about 1/8-inch in thickness. Cut crackers into desired shapes (squares and rounds) using small 1 1/4-inch cookie cutters. For the most authentic effect, cut with the fluted-edge side of cutter. Re-roll any excess dough and cut out additional crackers to avoid waste.

Place the cut-out shapes on the prepared baking sheets. Use a skewer or large toothpick to poke a hole through the center of each. Lightly sprinkle with sea salt, if desired.

Bake until golden brown around the edges, about 16-18 minutes, rotating the baking sheets halfway through baking. For crunchier crackers, bake for 20 minutes.

Remove from the oven and cool completely on the baking sheet before serving. Store leftover crackers at room temperature for up to 1 week. If tightly sealed, they’ll lose their crunch. Keep the lid slightly ajar to maintain some crunchiness.