In a nonstick pan on medium-low heat, cook the sausage on both sides until it is no longer pink in the middle and reaches an internal temperature of 160°F using a thermometer.
Heat the oil in a 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 melt.
Lightly toast the bagels.
Place the eggs and sausage on the bagel, cut in half and serve with oranges.