Heat a large skillet over medium heat. Cook the sausage patties for 4-5 minutes per side, or until browned and fully cooked. Transfer to a plate and keep warm.

While the sausage cooks, split the English muffins and toast them until lightly golden.

In a small bowl, whisk together the eggs, milk (if using), salt, and pepper.

Melt 1 tablespoon of butter in a nonstick skillet over medium-low heat. Pour in the eggs and gently stir until soft and just set, about 3-4 minutes.

Place a slice of cheese over each portion of eggs during the last minute of cooking, allowing it to melt slightly.

Spread the remaining butter on the toasted English muffins, if desired.

Assemble each sandwich by placing a sausage patty on the bottom half of an English muffin, followed by the cheesy egg. Top with the remaining muffin half.

Serve immediately while warm, or wrap each sandwich in foil or parchment paper for an easy grab-and-go breakfast.