Step 1: In a food processor, combine 1 1/4 cups flour, 1/4 cup fine or medium-grind cornmeal, 1/2 cup shredded Cheddar cheese, 1/2 cup (1 stick) unsalted butter (cut up) and 1 tablespoon sugar. Add 1/2 teaspoon salt and a few grinds of pepper. Pulse to a crumble.
Step 2: Drizzle in 2 tablespoons half-and-half. Pulse until mixture clumps into a soft dough. Add an additional 1 tablespoon of half-and-half, if needed.
Step 3: Preheat oven to 400 F.
Step 4: Pat dough into 2 disks. Set 1 disk on a sheet of parchment paper. Roll out and trim to a very thin 12-inch-by-12-inch square.
Step 5: Slide parchment paper onto a baking sheet. Use a pizza or pastry wheel to score dough into 36 two-inch square crackers. Sprinkle with a pinch of salt; press in lightly. Punch in neat rows of holes with a fork.
Step 6: Bake until crisp and golden, about 6 minutes. Cool crackers, then snap them apart (feel free to munch on a few). Repeat with remaining dough disk. Store crackers in a tin at room temperature.