Greek lemon soup; keep cooked rice in the freezer for speed. Cook some chicken stock with the rice, until the rice is very soft. Mix together juice of 1/2 to 1 lemon (depending on taste) and an egg. When the stock is ready, beat in the egg/lemon mixture and immediately turn off the heat. Salt to taste and garnish with parsley if you want.
Baked eggs; take a small ramekin. Layer in some of the following - cooked bacon or pepperoni or other cooked meat or meat substitute, a slice of tomato, fresh herbs, a bit of sliced onion, etc - top with one or two eggs, and a bit of cheese if you want. Slide into the oven or toaster oven until the eggs is almost done the way you like it.
Poached eggs in soup - in a small pan heat up some broth or leftover soup. When it's simmering well, crack in an egg or two, turn of the heat, cover and wait about five minutes. The egg yolk breaks into the soup and it's lovely and rich.
Poached eggs served on cooked whole grains tossed with lemon juice and chopped parsley or cilantro, drizzled with hot sauce. I use either soba (cooks quickly) or whole oats (not steel cut, takes about 20 minutes to cook, but freezes and re-heats well). Leftover rice would work well.
If you don't mind non breakfast food, you can always go with beans and legumes. Lentil soup, curried lentils (dhal) or chickpeas, beans and rice, bean burritos, hummus with veggie sticks or pita chips.
If you like tofu, check your Asian market or good grocery store for dou hua (豆花). It's a slightly sweet tofu custard that would be a good breakfast. There are also lots of sweet red or green bean dishes.
Or take cooked leftover meat and do a stuffed pita or sandwich.