Preheat the oven to 450 degrees F (230 degrees C). Line a baking sheet with parchment paper.

Whisk together flour, baking powder, baking soda, and salt in a large bowl. Cut butter into flour mixture with a pastry cutter or 2 knives until mixture resembles coarse crumbs. Stir in Cheddar cheese, Parmesan cheese, and onion. Pour in buttermilk; stir until evenly combined. Drop by 1/4 cupfuls onto the prepared baking sheet, about 2 inches apart.

Bake in the preheated oven until the tops of biscuits are lightly browned, 12 to 15 minutes. Serve warm.