Heat olive oil in large nonstick skillet over medium heat. Add onion and sweet red pepper; sauté 2 to 3 minutes. Reduce heat to medium-low; add potatoes, corn and hot red pepper and cook, stirring, until heated through. Transfer filling to a bowl and keep warm.
Melt 1 tablespoon butter in same skillet.
Beat together 2 eggs, 2 egg whites, half of water and 1/4 teaspoon of salt in bowl. Pour into skillet. Using a spatula, lift cooked mixture letting uncooked mixture flow underneath. When cooked, omelet should be barely brown on bottom and still moist in center.
Set aside 2 tablespoons vegetable filling for garnish. Spoon half of remaining filling over half the omelet and sprinkle with half the Cheddar cheese. Fold other half of omelet over filled half. Slip onto heat-proof serving platter, cover with aluminum foil and keep warm.
Repeat to make a second omelet.
Garnish each omelet with 1 tablespoon reserved filling. Cut each in half to make a total of 4 servings.