Heat oil in a non-stick skillet over medium heat, add green pepper and ham, cook until the pepper begins to soften, and the ham begins to brown, 3-5 minutes. Add potatoes, cook for 15 minutes, covered, stirring every 3-4 minutes. Stir in mushrooms, make 6 indentations in potato mixture, sprinkle cheese over the top, break an egg into each indentation and cook until eggs are the desired doneness. I cooked mine 10 minutes for yolks that were not runny (overhard).