Start by shredding your block of cheddar using the coarse side of a box grater. Freshly shredded cheese melts and blends far more smoothly into the dough than the bagged kind. Set it aside while you prep everything else.
Add the shredded cheese, softened butter, flour, salt, and paprika if using into your food processor. Pulse everything together until it looks like coarse, sandy crumbs. This usually takes about 15 to 20 short pulses.
With the processor running, drizzle in the ice water one tablespoon at a time. Stop as soon as the mixture clumps together into a ball, since too much water makes the dough sticky and hard to roll later.
Shape the dough into a flat disc and wrap it tightly in plastic wrap. Refrigerate for at least 30 minutes, which firms up the butter and makes rolling out the dough much easier.
On a lightly floured surface, roll the chilled dough out to about ⅛ inch thick. Use a pizza cutter to slice it into 1-inch squares, and poke a small hole in the center of each one with a toothpick so steam can escape while baking.
Arrange the squares on your parchment-lined baking sheet with a little space between them. Bake at 350°F for 12 to 15 minutes, until the edges turn lightly golden brown. Let them cool completely before digging in, since they crisp up more as they sit.