Preheat the oven to 425°F. Prepare two sheet pans with parchment paper, or grease them and dust them with flour.
Sift the flour, baking powder, sugar, pimentón (if using) salt, and baking soda in a large mixing bowl. Add the cold butter and, using a pastry cutter, a fork, or your fingers, work in the butter until the mixture resembles a course meal. Add the shredded cheese, then pour in the buttermilk and stir just until the mixture comes together—do not overmix.
Scoop the batter in ¼ cup portions onto the cookie sheets about 3 inches apart from each other. You should get about 16 biscuits.
Bake until golden brown, about 10-12 minutes. Cool on a rack, or serve them warm with butter. Store any leftover biscuits in an airtight container.