Heat half the oil in a non-stick pan over medium-low heat. Cook the sausage patty on both sides until it is no longer pink in the middle. Melt the cheese on top and place on the English muffin.
Add the remaining oil to the pan. Crack the eggs into the pan and cook until they start to set. Break the yolks and flip the eggs over to cook through. Season with salt and pepper. Once cooked, place on the english muffin and serve with oranges.