Halve and toast the bagel to your liking. Set aside.

Melt the butter in a small nonstick pan (ideally, small enough so it’s close to the diameter of your bagel, otherwise you can fold over the edges of the egg in the sandwich so it fits) over medium-low heat. Season the beaten eggs with a little salt and pepper, then add them to the skillet. Use a rubber spatula to stir the eggs so they cook evenly.

Once the eggs start to set, don’t disturb them. You want it to set almost like an omelet instead of being soft with small curds like regular scrambled eggs. Top with the shredded cheese, lower the heat to low, and cover, allowing the cheese to melt with the residual heat and steam. Fold the edges over as needed so the egg will fit inside the toasted bagel.

Spread the cut side of the bottom of your toasted bagel with pesto. Then top with tomato, caramelized onions and cooked bacon. Finish with the cooked eggs and then place the top half of the bagel over the bottom to enclose the sandwich. Slice in half if desired and serve immediately.