1–2 teaspoons hot sauce or mayonnaise per sandwich (optional)
Directions
Heat a griddle or flat-top to medium-high (375–400°F / 190–205°C). Add the oil or bacon grease and spread evenly.
Divide the sausage into four equal portions (about 4 oz / 113 g each) and gently roll into balls.
Place the sausage balls on the hot griddle. If using onions, scatter about 2 tablespoons over each ball. Using a sturdy spatula or burger press, firmly smash each ball into a thin patty (about ¼-inch thick).
Cook undisturbed for 2–3 minutes, until the edges are deeply browned and crispy.
Flip the patties. Season with half of the salt and pepper. Cook 1–2 minutes more, or until the internal temperature reaches 160°F (71°C).
Place one slice of cheese on each patty and let melt, about 30 seconds.
Butter the cut sides of the English muffins and toast on the griddle for 1–2 minutes, until golden brown. Remove and set aside.
Crack the eggs onto the griddle. Season with the remaining salt and pepper. Cook 2–3 minutes for over-easy. Cook 3–4 minutes for over-medium.
Layer the bottom muffin half with a sausage patty and melted cheese, then a fried egg. Add hot sauce or mayonnaise if desired. Top with the remaining muffin half and serve immediately.