Directions
Step 1
Heat 2 tsp oil in large cast-iron skillet on medium. Add onion and cook 3 minutes. With wet hands, shape sausage into four 1/4-inch-thick patties, add to skillet with onion, and increase heat to medium-high. Flip onion and cook until just tender, 2 to 3 minutes more. Cook patties until browned, 2 to 3 minutes, then flip.
Step 2
Separate onion slices into rings and arrange on top of patties, then top with Cheddar and continue cooking until sausage is cooked through, 2 to 3 minutes more.
Step 3
Meanwhile, heat remaining 2 teaspoons olive oil in large nonstick skillet on medium and cook eggs to desired doneness, 4 to 5 minutes for runny yolks. Top bottom halves of muffins with sausage, then eggs, pepper slices, and parsley