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Find a different recipe. Beef bouillon is one of the nastier things in a modern kitchen. I would argue that plain old water would produce better results than any broth made with beef bouillon.
Maybe better questions would be "What role do egg whites play in baking?" and "What role do egg yolks play in baking?"; that's angel vs. pound cake dichotomy.
A basted egg is better than "over easy" any day. Basting will completely cook the white and leave the yolk deliciously golden and runny. Isn't that what you're looking for an an over easy egg?
