Spray a 10-inch, nonstick, ovenproof skillet with cooking spray. Add the onion, bell pepper, and ham to the skillet. Place the skillet over medium heat. Cook, covered, for about 3 minutes, stirring often until the onions and peppers begin to soften.
Stir in the potatoes and reduce the heat to medium. Without stirring, cover and cook for 1 minute until the mixture is heated thoroughly.
Reduce the heat to low. Pour the egg mixture over the potato mixture. Without stirring, cook, covered, for about 10 minutes until the eggs are nearly set.
Remove the skillet lid and wrap the handle in aluminum foil. Place the skillet under a preheated broiler 6 inches from the heat for about 3 minutes until the eggs are completely set.
Top with cheese and broil 1 minute until the cheese has melted.
Cut the frittata into wedges and serve immediately.