I'm sure many families have their own version of an egg sandwich, and we have more than one. This particular version is more truly a sandwich. I adapted it a bit from our English muffin version with an egg over easy so it could be eaten "on the go." It can be made in less than 10 minutes.
Salt and pepper, to taste
1 slice American cheese
2 slices bread (I use Arnold whole wheat)
Butter, to taste (we love Brummel and Brown)
1. Spray small skillet with cooking spray, even if it's a non-stick skillet. Crack eggs into skillet (they should touch) and begin cooking between medium & medium-high heat (the higher the heat the closer you will need to watch to avoid burning). Add salt and pepper.
2. When you notice some bubbling in the egg whites and browning around the edge, add cooking spray to the top of the eggs and see if your non-draining spatula will allow you to CAREFULLY flip the eggs over, picking up the skillet and tipping it a bit so the yolks don't have as far to "flop" and are less likely to break. (If the egg's not ready, try again in a bit.)
3. Add salt and pepper to this side. Put the slice of cheese on top (eventually melting it).
4. Put the bread slices in the toaster. (My toaster toasts plenty on its lowest setting; you may need to adjust the time at which you toast according to how toasty you like your bread.)
5. Break the egg yolks so that you don't have to worry about them dripping while you're eating on the go (they will get a chance to cook just long enough during the next step...). Why bother not breaking them until now? --I guess I prefer the slightly different taste, so I avoid "overcooking" the yolk.
6. Add butter to one side of each bread slice (butter sides in once the sandwich is made so you don't get it on your hands).
7. Add the eggs and cheese (maybe doubled over to fit the bread) to one bread slice, flip the other bread slice on top, and voila! Grab a paper towel and go! [I mean, enjoy your lovely protein-packed sandwich?... ;) ]
Source: adapted from joint effort by the hubs and me (Ok, mostly the hubs. And then I adapted it to make this version.)