In a skillet over medium heat, cook the bacon slices until they are crispy and golden brown. Remove from the skillet and place them on a paper towel-lined plate to drain off any excess grease.
While the bacon is cooking, toast the bagel halves until they are golden brown and crispy. You can do this in a toaster or under the broiler in your oven.
In a small bowl, whisk together the eggs until they are well beaten. Season with salt and pepper to taste. In the same skillet used to cook the bacon, melt a little butter or heat a small amount of cooking spray over medium heat. Pour the beaten eggs into the skillet and cook, stirring occasionally, until they are scrambled and cooked through.
Place a slice of cheese on the bottom half of each toasted bagel. Top with a generous portion of scrambled eggs, followed by two slices of crispy bacon. Finally, place the top half of the bagel over the bacon to form a sandwich.
Serve the breakfast sandwiches immediately while they are still warm and the cheese is gooey. Enjoy them as-is or pair them with your favorite breakfast sides, such as fresh fruit, hash browns, or a hot cup of coffee.