Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Combine the flour, Cheddar, smoked paprika, cayenne and 1/2 teaspoon salt in a food processor and pulse to combine. Add the butter and pulse until incorporated. Add the heavy cream and process until the dough forms a ball.
Lightly flour a sheet of parchment paper and place the dough on top. Shape the dough with your hands into a flat rectangle, then lightly flour the dough. Roll it out with a rolling pin until it is a little less than 1/4 inch thick (about a 12-by-9-inch rectangle). Cut the dough into squares or rectangles and carefully transfer to the prepared baking sheet. Sprinkle the dough pieces with about 1/4 teaspoon more salt, gently pressing it into the surface, then dust very lightly with more smoked paprika. Bake until light golden brown, 10 to 12 minutes. Cool completely on a rack.