Slice bagel in half and spread butter on the inside.
Preheat pan or griddle over medium heat and toast the bagels until golden brown. If using a toaster oven, toast the bagels before adding the butter.
Use the remaining tablespoon of butter to grease the preheated pan. Cook eggs over-hard. Season with salt and pepper.
Layer the cheese and the bacon on top of one the eggs and use a spatula to flip the other egg on top of the bacon. Let sit for a few seconds to let the cheese melt.
Once the cheese has melted, complete the bagel sandwich.
Serve immediately or wrap for an on-the-go breakfast.