Prepare a rimmed baking sheet with parchment paper or aluminum foil for easy clean up.
Split the bagels in half and place on the prepared baking sheet.
Beat the eggs along with the milk, salt, and black pepper.
Heat a large skillet over medium to medium-high heat.
Add the butter to the heated skillet, and add the beaten eggs.
Lightly scramble the eggs, keeping them slightly undercooked and soft so they spread on the bagel easier. (they will keep cooking in the oven)
Spread the egg over the bagel halves.
Top with a bit of cubed ham.
Sprinkle the shredded cheese over the ham. You can press down lightly on each breakfast bagel to help it all stay in place.
Bake the bagels until the cheese has melted. About 5 to 8 minutes.
Notes
Serve breakfast bagels right away, place the breakfast bagels in an air tight container and store for a day or two in the refrigerator, or freeze for later use.When reheating the breakfast bagels in the microwave, do it in 20 second increments since all ovens vary. Be careful about over heating.