Heat oil in large nonstick skillet on medium heat.
Add vegetables; cook 5 min. or until potatoes are lightly browned, stirring occasionally.
Add eggs, 1 at a time, to skillet, spacing eggs evenly over potatoes; cover. Cook 3 to 4 min. or until egg whites are set and yolks begin to thicken but do not become firm.
Sprinkle with cheese; cook, covered, 1 min. or until melted.