American
Divide the sausage meat into 4 portions and press each into a thin patty about 10 cm wide, a little wider than the muffins, as they shrink when cooked.
Fry the patties in a frying pan over medium heat for 3-4 minutes per side, until browned and 71C in the center; drain on paper towels and pour the fat out of the pan.
Split the English muffins, toast them and spread the cut sides with half of the butter.
Melt the remaining butter in the pan over medium-low heat, set 4 greased egg rings in it and crack an egg into each; pierce the yolks and season with a pinch of salt and pepper.
Cover the pan and cook for 3-4 minutes, until the eggs are set, then remove the rings.
Lay a cheese slice on each hot sausage patty so it softens.
Build each sandwich from the bottom muffin half, the sausage with cheese, the egg and the top half, and serve hot.