In the skillet, melt butter on medium high heat. Add potatoes and, using a spatula, turn to coat them in the butter. Cook for 2-3 minutes, turn and continue to cook until they appear defrosted. Add onions and peppers to potatoes. Put on lid and cook on medium heat for 2-3 minutes until brown bits appear on the underside, then turn and continue to cook with the lid on until browned on the second side; you may add pepper and/or salt to taste. Turn the mixture one more time and crack 4 eggs on top; keep them separate along the outside of the pan. Reduce heat to low-medium and cook until the yolks are done to taste. Remove from heat and shred the meat over the eggs and mixture, then top with cheese and let set until the cheese melts. Cut into quarters, each having an egg, and serve.