Adjust oven rack to middle position and heat oven to 450°.

Place dry ingredients into a bowl and whisk to blend. Hold a cheese grater over the bowl and grate the chilled butter on top of the dry ingredients. With your fingertips, lightly “fluff” flour and butter together, so that you have individual small pieces of butter coated with flour. Now use a firm rubbing pressure with your fingertips to work some of the mix into a sandy texture.

Stir in buttermilk and milk, transfer to floured board, and knead just a few strokes to make it all come together. Roll or pat into a rectangle just less than a half-inch thick. Cut rectangle in half, place one half over the other, and again roll to a half-inch thick.

Lightly grease biscuit cutter, then put some flour into a dish just large enough to hold cutter. For each biscuit, dip cutter into flour then cut biscuit with one decisive punch. If using a round cutter, form leftover dough into another rectangle, with as little handling as possible and cut more biscuits. Place biscuits 1” apart on ungreased sheet, brush tops with melted butter.

Bake until lightly browned, 10–12 minutes.