Sometimes it can be tough to get toddlers to eat enough protein. If Goose asks for eggs in the morning, I'm happy to oblige! The problem is that she wants eggs NOW . . . and though we're working on patience, first-thing-in-the-morning hungries are pretty rough.
To get breakfast on her high chair tray FAST, I use the microwave to cook a scrambled egg. I use a round glass dish, around four inches across. (I used to use plastic, but I think this method is pretty hard on them.) Grease it according to your favorite method, or whatever strikes your fancy in the morning - nonstick spray, bacon grease, butter, etc.
You can crack the egg directly in the dish and scramble it with a fork, or you can crack it into another bowl or cup, scramble, then add to the dish. The advantage of using a separate bowl is that you don't disturb the grease and the egg sticks a bit less, though I've found that either way I still need to handwash the bowl.
I start by microwaving for 30 seconds on high, then let the egg rest a bit to deflate. If it's a smaller egg, it may be cooked through; I usually give it another 10-20 seconds to make sure. (Runny eggs make me nervous.) Run a knife around the outer edge of the egg to loosen it from the bowl and tip it out onto a plate, then cut into pieces.
(EDIT: These are also perfect with cheese and bacon, sausage, or ham on biscuits or bagels! And now that Goose is older, I crack two eggs in the bowl and cook it for longer - a minute to a minute and a half, depending on size.)
And, if you're my Goose, holler for "sirup!" (a combo of honey and real maple syrup thinned a bit with water) in which to dip your toast and egg . . . then go to Tammy's Recipes for more kitchen tips.