Preheat oven to 425°F (220°C).
Whisk together flour, baking powder, sugar, and salt in a bowl.
Cut in cold butter using a pastry cutter or fingers until mixture resembles coarse crumbs.
Add cold milk and gently mix until dough just holds together.
Turn dough onto a floured surface, pat to about ¾ inch thick, and cut biscuits with a round cutter.
Place biscuits on a baking sheet and bake for 12–15 minutes until golden and fluffy.
In a skillet over medium heat, cook sausage, breaking it up, until browned and cooked through; do not drain fat.
Sprinkle flour over cooked sausage and stir to coat, cooking for 1 minute.
Gradually pour in milk while stirring constantly to avoid lumps.
Simmer gravy for 5–7 minutes until thickened, then season with salt, pepper, and optional cayenne or paprika.
Split warm biscuits in half and spoon sausage gravy generously over them.
Serve immediately while hot.