Using a small lid (we used a plastic cap from our glass milk jars, but a lipton iced tea cap or it's equivalent would do) cut a round hole out of the center of a piece of bread- preferably whole grain!
Break an egg into the center space.
Some of the egg will likely spill out onto the surrounding bread. This is a good thing :) Place another slice of bread on top, buttered side facing up. Note- the second piece of bread does not need to have a hole cut.
Cook for a minute on each side, and voila! The dippy spreads throughout the sandwich as you eat it, and remains self-contained. It's the best! Now if I could just come up with a clever use for that remaining piece of bread....any suggestions?!