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Make circles from the vegetable. Use the larger outer rings for the egg ring.  Add cooking fat of choice. Cook until the egg is at the firmness of your liking. You can eat the vegetable ring too, or remove it as preferred.
Slice the onion or bell pepper across the width. If using an onion, pop out all of the inner rings. If using a bell pepper, pull out any center pith and seeds. Place the vegetable circles into the frying pan or skillet being used for cooking on the campfire or camp stove. Crack the egg into the middle of the vegetable ring. Remove.