Preheat your oven to 375°F. Grease a 9x13-inch baking dish. Set aside.
In a large mixing bowl, whisk together the eggs, milk, salt, garlic powder, onion powder, and pepper until well combined. Set aside.
In a large skillet, sauté the diced ham, green onion, green bell pepper, and red bell pepper until the vegetables are tender and the ham is lightly browned. Turn off the heat.
Add 1 1/2 cups of the cheese and the thawed hash browns to the ham mixture. Mix until combined.
Pour the ham and hash brown mixture into the greased baking dish. Set aside.
Pour the eggs over the ham and hash brown mixture.
Sprinkle the remaining 1/2 cup of shredded cheese evenly over the top.
Bake the casserole in the preheated oven for 45-50 minutes at 375°F, or until the eggs are set and the top is golden brown.
Let the casserole cool for a few minutes before slicing and serving. Top with additional sliced green onions if desired.