In a small skillet, cook the sausage patty until browned on both sides and cooked through. Set aside.
Add the butter to the pan, and swirl the pan to ensure that the butter covers the cooking surface. Add the beaten egg and season with salt and pepper. Tilt the skillet around so that the egg is thin and reaches the edges of the bottom of the pan. Cook the egg until it has set, and the top surface is just barely still wet.
Place the sausage patty on top of the egg and fold the egg in quarters around it (so the sausage is wrapped up in the egg). Top with a slice of cheese and transfer to the english muffin. Wrap in wax paper and place in the fridge or freezer.