In a medium-sized saute pan over medium heat, melt the butter then add the diced onions and bell peppers. Saute until translucent, about 5 minutes, then remove from the heat and set aside.
In a large bowl, combine the eggs, milk, salt and pepper and beat with a whisk or fork to break up the eggs. Add in the diced ham and shredded cheese and stir to combine.
Spray a 9" x 13" baking dish with non-stick cooking spray, then add the sautéed onions and peppers evenly over the bottom. Pour the egg mixture over the onion mixture and gently stir to combine.
Bake in the preheated oven for 25-30 minutes, or until the edges are golden brown and the eggs in the middle of the baking dish are set.
Remove from the oven and let cool for a few minutes before slicing. Serve with a dollop of sour cream, diced tomatoes and avocados if desired. Enjoy!