In a food processor, briefly pulse flour, salt, and sugar. Add butter and cheddar; pulse until mixture resembles coarse meal, with a few pea-size pieces of butter remaining. Sprinkle with 2 tablespoons ice water. Pulse until dough is crumbly but holds together when squeezed (if necessary, add up to 2 tablespoons water, 1 tablespoon at a time). Don't overmix.
Divide into two disks. Turn dough out onto a large piece of plastic wrap. Fold plastic over dough; press to shape into a 1-inch-thick disk. Refrigerate until firm, at least 1 hour (or up to 3 days). See Cheddar-Crusted Apple Pie for rolling and fitting instructions.