Heat the oven to 400°F (200°C). Grease a 9-by-13-inch baking dish with butter or cooking spray. Set it aside where you can reach it easily.
Brown the sausage. Set a large skillet over medium heat and add the sausage, breaking it up with a spoon. Cook until well browned with crispy bits, about 6 to 8 minutes. If you see more than about 2 tablespoons of fat in the pan, spoon off the excess. If it looks a little dry, add a tablespoon of butter.
Make the roux. Sprinkle the flour over the sausage and stir it in so it coats everything. Let it cook for 1 to 2 minutes, stirring now and then. This step cooks out the raw flour flavor and keeps the gravy smooth.
Add the milk. Slowly pour in the milk while whisking or stirring, scraping up any browned bits from the pan. Keep the heat at medium. The gravy will look thin at first, then thicken as it gently bubbles, about 5 to 7 minutes. You’re aiming for thick but pourable, like a loose Alfredo sauce.
Season. Stir in the salt, black pepper, garlic powder, onion powder, cayenne, and thyme. Taste and adjust the salt and pepper. If using cheddar, stir half of it into the gravy now so it melts.
Build the bake. Spread about 1 cup of the gravy into the bottom of the prepared baking dish. Scatter the biscuit quarters evenly on top. Pour the remaining sausage gravy over the biscuits, nudging things around so most pieces are coated. Sprinkle the rest of the cheddar over the top.
Bake. Slide the dish into the oven and bake until the biscuits are puffed and cooked through and the top is golden in spots, about 18 to 22 minutes. If the top is getting dark before the biscuits are done, tent the pan loosely with foil for the last few minutes.
Rest and serve. Let the bake rest for 5 to 10 minutes so the gravy settles a bit. Shower with chives or scallions. Serve warm, straight from the dish. A little hot sauce on the side never hurts.