Preheat a nonstick skillet over medium heat. Spray with cooking spray then add the potatoes, onions, and green pepper.
Season with the garlic powder, onion powder, salt, and pepper.
Cook for 10 minutes, stirring occasionally. During the last two minutes of cooking time stir in the ham. (Cooking time for the potatoes will depend on the size. Make sure to test the potatoes before adding the eggs.)
Make four pockets in the potato mixture. Add one egg to each pocket.
Sprinkle the shredded cheese over the potato mixture. Cover with a lid and let the potatoes cook for 3 minutes, or until the egg white is set.