Heat a non-stick pan over medium heat. Brown the Canadian bacon on both sides. Then place on the bagel.
In the same pan add the oil. Crack the eggs into the pan (crack the yolk or keep it whole as desired). Cook until the whites of the egg start to become firm. Flip the egg over and top with cheese. Cook until the cheese is melted. Cover with a lid to help the cheese melt faster. Season with salt and pepper.
Portion the eggs onto the bagel and cut in half. Serve with nectarine.