Slice the bagel in half. Lightly toast it in a toaster or toaster oven.
In a small nonstick frying pan, cook the egg over medium high heat, turning once. Season with salt and pepper.
Spread pesto on the toasted bagel. Top one half of the bagel with the egg and cheese slice.
Heat the lunchmeat in the nonstick fry pan, then add it to the bagel on top of the cheese.
Finish the sandwich by topping it with the other bagel half.