Prepare bacon or sausage in skillet, according to package directions. Remove from skillet and cover to keep warm. Drain grease but don’t wipe out skillet. Place the bagels sliced-side down in the skillet and toast over medium heat until lightly browned. Remove from skillet and set aside.
Cook eggs in the same skillet to your liking (recommended: over-easy or over-medium). Layer each breakfast sandwich as follows: Bottom bagel slice, 1/2 of the cooked meat, 1 cooked egg, slice of cheese, toppings as desired and top bagel slice.