So, new favorite breakfast sandwich at our house, at least among those that can eat eggs. I think that this would be hard to do without dairy, but you might be able to if you had a good substitute cheese that would melt well and help hold things together. Could be made vegetarian as long as you are ok with dairy and eggs.
Ingredients:
Safe bagel (I use everything bagels)
Butter/butter spread (I use Earth Balance soy free just because it is easier to spread out of the fridge)
Two eggs
Slice of cheese of your choice (I use pepper jack, colby jack or cheddar)
Breakfast meat of your choice, cooked through (I have used deli ham and bacon. Canadian bacon or a sausage patty should work as well.)
Toast the bagel and spread with butter.
Spray a large pan with non-stick spray and heat for 30-45 seconds over medium heat. Crack two eggs into the pan, keeping them as separate as possible. Salt and pepper the eggs. Add a bit of water to the pan for steam and cover until the whites are cooked. Uncover. Poke a small hole in the side of the yolk just to let it flatten a bit - I keep most of the yolk liquid. Place the breakfast meat (if desired) on top of one of the eggs, and then top with sliced cheese. Add a little bit more water to the pan for steam and cover just until the cheese is melted. Flip the plain egg over on top of the egg with the meat and cheese, yolks towards the inside. Place the eggs on the bottom half of the bagel and top with the other half.
My family (DH, DSD, my Mom and brother) prefer this cooked with the yolk still mostly liquid. If DH is eating in the car or while working from home I will cook the eggs more for less potential mess, and you could definitely cook to your personal preference. Everyone I have made it for likes it well enough that I can serve it for an easy quick dinner as well.
This is a pretty heavy, bulky sandwich. DSD is a lighter eater, and prefers it with a less dense brand of bagel so she can finish it.