Heat the oil in a large non-stick skillet over medium heat. Add the vegetables; cook 5 minutes or untl potatoes are lightly browned, stirring occasionally.
Add eggs, 1 at a time, to skillet, spacing eggs evenly over potatoes; cover. Cook 3 to 4 minutes or until egg whites are set and yolks begin to thicken but do not become firm. Salt and pepper the eggs, if desired.
Sprinkle with the cheese; cook, covered, 1 minute more, or until melted.