Cut the peppers in slices lengthwise about 1/2 inch wide (deveining and removing the tops too). Clean with water and pat with paper towels.
Heat vegetable oil in a pan, and add peppers, fry 5 to 10 minutes, letting them soften, but not brown. When they are done, remove from the pan, draining some oil from them.
Scramble eggs, adding 1 to 2 T. of water.
In an omelet pan melt butter, adding the peppers in a single layer around the pan. Heat until butter simmers.
Then add the scrambled eggs. As omelet cooks, draw the edges towards the center, letting the loose eggs to roll to the outer edge of the pan. When the bottom of the omelet appears cooked (do not brown!), cover the omelet pan with the large dish and invert the pan onto the plate. Now slip the omelet back into the pan so the topside can cook.
Remove the omelet to a clean plate. Salt and pepper to taste.
Pepper and eggs may be eaten plain, but are best served in sandwiches on crusty Italian bread.
NOTE: A similar dish is made with potatoes, frying them up first and then adding the eggs.