4 cups all-purpose flour (spooned and leveled), plus more for rolling
2 T. baking powder
1 tsp. baking soda
1 3/4 tsp. fine salt
6 oz. sharp cheddar or Gruyere, grated (1 1/2 cups)
3/4 cup (1 1/2 sticks) cold unsalted butter, cut into 1/2-inch pieces
3 T. chopped fresh chives
1 1/2 cups cold buttermilk

Preheat oven to 450 degrees. In a food processor , pulse flour, baking powder, baking soda, and salt until combined. Add cheese, butter, and chives; pulse until mixture resembles coarse meal, with a few pea-size pieces of butter remaining. Add buttermilk and pulse until combined (do not overmix). Turn dough out onto a lightly floured work surface and knead until it just comes together. With a floured rolling pin, roll out dough 3/4 inch thick. With a floured 2 3/4-inch biscuit cutter, cut out 16 rounds (reroll and cut scraps). Place biscuits, 1 1/2 inches apart, on a baking sheet and bake until puffed and golden, 13 to 15 minutes. Transfer to a wire rack and let cool slightly. Serve warm or at room temperature.