Preheat oven to 450°F. Whisk together flour, baking powder, baking soda and salt in a mixing bowl. With a pastry blender or 2 knives, cut in cheese and butter until pieces resemble small peas.
Make a well in center of flour mixture and add buttermilk. With a fork, toss gently until mixture is just moistened; dough will be very sticky. Do not over mix.
Turn dough out onto a wellfloured work surface and knead very lightly once or twice with floured hands, sprinkling dough lightly with enough flour to keep it from sticking. Using floured hands, gently but firmly pat out dough 1/2 inch thick.
Dip a 2-inch biscuit cutter into flour and cut out biscuits, dipping cutter into flour as necessary. Gather scraps and repeat. Transfer biscuits to an ungreased baking sheet and bake until golden brown, 12 to 15 minutes. Serve warm.