Get the oven ready: Heat the oven to 400°F with a rack in the middle position.

Prep the finish: Slice the scallions, shred the cheddar if needed, and set the bread aside for later.

Start the skillet: Set a 10-inch ovenproof skillet over medium heat on the stove.

Brown the sausage: Add the sausage to the hot skillet. Cook for 4 to 5 minutes, breaking it into small pieces with a wooden spoon, until it is browned and no longer pink.

Cook the onion: Add the chopped onion to the skillet. Cook for 3 to 4 minutes, stirring often, until the onion softens and looks glossy.

Add the butter: If the skillet looks dry, add the butter. Let it melt into the sausage and onion mixture.

Build the gravy base: Sprinkle the flour over the sausage mixture in the skillet. Stir for 1 minute so the flour coats the meat and onion and loses its raw look.

Add the milk: Pour the milk into the skillet a little at a time, stirring well after each addition so the gravy stays smooth.

Thicken the gravy: Stir in the black pepper and salt. Keep the skillet over medium heat and cook for 2 to 3 minutes, stirring, until the gravy thickens enough to leave a short trail when you drag the spoon across the bottom.

Season the skillet: Turn off the heat. Taste the gravy and add a little more salt or pepper if it needs it.

Make spaces for the eggs: Use the back of the spoon to make 6 shallow wells in the gravy so the eggs have a place to sit.

Add the eggs: Crack 1 egg into a small bowl, then slide it into 1 well in the skillet. Repeat with the remaining eggs, spacing them evenly across the gravy.