Heat a nonstick skillet on medium heat and cook the sausage on both sides until it is nicely browned and reaches an internal temperature of 160°F (71°C) using a thermometer.
Preheat the oven broiler on low.
Toast the English muffins.
Heat the oil in an oven-safe nonstick pan on medium heat. Crack the eggs into the pan; season with salt and pepper. Cook until the whites start to become firm, then flip the eggs over, add the sliced cheese, and place under the broiler to melt.
Place the eggs and sausage on the English muffin and enjoy with orange juice.