Preheat oven to 450°F and line a baking sheet with parchment paper.
In a large bowl, sift together 3 cups all-purpose flour, 4 1/2 teaspoons baking powder, 3/4 teaspoon baking soda, and 1 1/4 teaspoons salt.
Add 4 ounces cold unsalted butter, cut into cubes. Using a pastry blender, two knives, or your fingertips, cut the butter into the dry ingredients until the mixture looks like coarse peas.
Pour in 1 cup cold buttermilk and stir gently with a spatula or wooden spoon until the dough just comes together. If the dough seems dry, add additional cold buttermilk a little at a time until it holds together.
Turn the dough onto a lightly floured surface (use extra flour for dusting) and pat it into a rectangle about 1 inch thick. Handle the dough as little as possible.
Dip a 2-inch round cutter into flour and cut straight down into the dough without twisting. Re-roll scraps as needed and repeat cutting.
Place the biscuits on the prepared baking sheet. For soft sides, set them so they touch; for crusty sides, space them about 2 inches apart.
Brush the tops of the biscuits with melted butter.
Bake in the preheated oven until the biscuits are puffed and lightly golden, about 12–16 minutes.
Remove the biscuits from the oven, brush with additional melted butter if desired, and serve warm.