Preheat the oven to 450°F (232°C).
Combine the flour, baking powder, baking soda, and salt in a bowl.
Cut in the cold butter until the mixture resembles coarse crumbs.
Stir in the buttermilk until just combined.
Turn the dough out onto a floured surface and gently knead it.
Pat the dough to about 1-inch thickness and cut out biscuits.
Arrange the biscuits on a baking sheet and bake for 12-15 minutes.
While the biscuits bake, prepare the sausage gravy.
Cook the sausage in a skillet over medium heat until browned.
Sprinkle the flour over the cooked sausage and stir well to combine.
Gradually add the milk while stirring constantly.
Bring the mixture to a simmer and cook until thickened, about 5-10 minutes.
Season the gravy with black pepper and cayenne to taste.
Serve the biscuits warm, topped generously with sausage gravy.