Preheat an oven to 450 degrees F (230 degrees C). Line a baking sheet with parchment paper.
Whisk the flour, baking powder, baking soda, and salt together in a bowl. Cut the butter into the flour mixture until the mixture resembles course crumbs. Stir the onion, Parmesan cheese, and Cheddar cheese into the flour mixture. Pour the buttermilk into the bowl; stir until evenly combined. Drop by 1/4-cupfuls onto prepared baking sheet, about 2 inches apart.
Bake in the preheated oven until the tops of the biscuits are lightly browned, 12 to 15 minutes. Serve warm.
