Heat olive oil in a large nonstick skillet over med-high heat. Add the onions and cook until softened. Stir in the peppers and sauté 2-3 minutes. Add the ham and cook for an additional 1-2 minutes. Transfer to a large mixing bowl. Gently stir in the hash browns and cheese.
Spread the hash brown mixture in a 13 x 9 inch baking dish coated with cooking spray. Set aside.
In a large bowl, whisk together the eggs, milk, garlic powder, onion powder, salt and pepper. Pour the egg mixture over the hash browns. Bake the casserole for 50-55 minutes or until puffy, golden and firm in the center.