Add shredded cheddar, flour, cornstarch, and salt together in a food processor until combined. Add butter and process until mixture resembles wet sand. Add water and pulse until dough forms large clumps, about 10 pulses. Transfer dough to a floured surface. Divide in half and wrap each in plastic wrap and refrigerate until firm, about 45 minutes.
Preheat oven to 350°F and line two baking sheets with parchment paper. Unwrap each dough ball. Place each on a lightly floured work surface and roll out into about a 9-inch square. Using a sharp knife, trim dough into a neat 8-inch square. Each 8-inch square will have 64 squares (crackers). Place squares on prepared baking sheet. Lightly sprinkle with sea salt. Bake until golden brown around the edges, or about 16-18 minutes. Remove from oven to cool completely.
Store leftover crackers at room temperature for up to 1 week. To re-crisp crackers, throw them back into the oven again for several minutes.