Lightly cover one side of foil with cooking spray. Place 1/2 of bagel crust-side down in the center of each foil square. Cup the foil around the bagel leaving the top completely open.
Beat the eggs, milk, and seasoning. Slowly pour 1/4 of the mixture over each bagel. Place 1/4 of the diced ham on each bagel; cover with a slice of cheese. Bake bagels on a cookie sheet at 350 degrees for 35 to 40 minutes or until eggs are set and cheese is melted.