Cook the sausage - Heat a skillet over medium heat. Add the sausage patties and cook for 3-4 minutes per side, until they develop a nice brown crust and are cooked through completely. The patties should reach an internal temperature of 160°F (71°C). Remove from the skillet and set aside on a plate.

Toast the buns - Split the English muffins in half and place them cut-side down in the same skillet to toast for 1-2 minutes until they turn golden brown. This allows the muffins to absorb some of the sausage flavor while creating a crispy texture that prevents sogginess. Remove and set aside.

Cook the eggs - Melt 1 tablespoon of butter in the skillet over medium heat. If using milk, whisk it with the eggs in a small bowl before adding to the pan for extra fluffiness. Crack the eggs into the skillet and scramble them gently with a spatula. Season with salt and pepper to taste. Cook until the eggs are just set but still slightly moist, about 2-3 minutes. Be careful not to overcook as eggs will continue cooking slightly after removal from heat.

Assemble the sandwiches - Place two sausage patties on the bottom half of each English muffin. Layer with a portion of the cooked eggs, then top with a slice of cheese. Cover with the top half of the muffin to complete the sandwich.

Optional melt - For extra melty cheese, return the assembled sandwiches to the skillet over low heat. Cover with a lid for 30-60 seconds, allowing the cheese to melt completely while warming all components together. This creates the perfect melty consistency that binds all ingredients together.