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Preheat the oven to 375°F and line a baking sheet with parchment paper.
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Combine the flour, cornmeal, baking powder, and salt in a medium bowl. Rub or cut in the butter until no large chunks remain. Add the shredded cheese and toss to distribute evenly, then stir in the buttermilk until the mixture is just moistened.
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Drop the mixture onto the prepared baking sheet, 1/4 cup at a time, leaving about 2 inches between each to accommodate spreading as the biscuits bake. Bake for 25 to 30 minutes, or until the tops of the biscuits are golden brown.