Preheat oven to 475 degrees and grease a loaf pan (or if doubling the recipe, a round cake pan should work).
Melt butter in microwave and let cool for about 5 minutes.
Meanwhile, mix flour, baking powder, baking soda, sugar, and salt in large bowl. Mix cold buttermilk and milk with butter, stirring until butter forms small clumps.
Add wet mixture to dry ingredients and stir until just incorporated. Do not overmix.
Pour extra flour onto a plate or shallow bowl. Rub your hands in the flour to dust them well. Spoon a lump of wet dough (around 1/4 cup) into the flour, and sprinkle some flour over it to coat well. Gently pick it up and shape it into a soft round by tossing the dough gently back and forth between your hands. Place biscuit in pan and repeat with remaining dough, ensuring biscuits touch each other. This keeps them soft and ensures they rise nicely.
Bake until tops are golden brown, 10 - 12 minutes. You can brush with an additional melted butter if desired. Cool for a minute or two, then dump out and break apart into individual biscuits.