To the bowl of a food processor, add the flour, sugar, baking powder, salt, and baking soda. Pulse until combined. Add the butter pieces and process until mixture resembles fine meal. With the machine running, add buttermilk and process just until dough comes together.
Turn dough out onto a board and knead briefly; do not overwork dough, or biscuits will be tough. With a rolling pin, roll dough out to a 1-inch thickness. Flour a 1-inch round cutter, and then cut out biscuits and transfer to a sheet pan. Refrigerate for 1 hour, or up to 24 hours. Brush tops of biscuits with milk. Bake for about 30 minutes, or until lightly golden on top.