Preheat oven to 325 degrees. Pulse butter, cheddar, flour, salt, cayenne pepper, and paprika in a food processor until mixture resembles coarse crumbs. Add heavy cream; pulse until just combined.

Divide dough into 4 pieces; shape into rectangles. Wrap each in plastic. Refrigerate until firm, about 30 minutes.

Working in batches, roll out each rectangle on a lightly floured surface to a 1/4-inch thickness, and cut into 1-inch squares. Transfer to a baking sheet leaving at least 1/4 inch between each. Refrigerate until chilled and firm, about 20 minutes. Bake until pale golden, 15 to 17 minutes.