I would try to doctor the oatmeal....I put applesauce and cinnamon in ours....and dd loves to add the applesauce herself. She likes to toss a few raisins in there too.

French toast (eggy bread) is great,,,esp if you cut it in shapes, soldiers, circles (use a glass) or use a cookie cutter. I always found at that age that presentation was everything! Dipping into syrup is so much more fun that me putting it on for her!
I have a really simple, wholesome and hearty banana muffin recipe....a few mini muffins and a yogurt is one of dd's fave breakfasts.
For the constant asking for food....at around age 3.5 I put a tray in the fridge for dd full of stuff she could help herself to, any time she wanted. Carrrot sticks, celery, yogurt, grapes, hard boiled egg, oranges, etc. She loved getting things herself, and she loved that the tray was "just for her." I didn't like telling her she couldn't possibly be hungry, but I knew she wasn't, if it was like 20 minutes after breakfast or lunch! So supplying the tray removed me from the equation, and she loved serving herself.