Combine mayonnaise and Dijon mustard in a small bowl.
Heat butter in a nonstick pan. Whisk eggs and season with salt and pepper. Add eggs to pan and use a rubber spatula to gently move eggs around the pan as they cook. Once almost cooked, sprinkle cheese on top of eggs so that it will melt.
Push eggs to one side of pan and add ham slices to other side of pan to warm them. Turn heat off.
To assemble spread a small amount of mayo mixture on one bagel half for each sandwich. Top with spinach, ham, and cheese-topped eggs. Place remaining bagel halves on top and serve.
This recipe originally appeared on spicysouthernkitchen.com