Preheat oven to 375 degrees.
Add the oil to mushrooms, onions, and peppers in a skillet. Cook for 8-10 minutes until tender. Remove from heat.
Whisk eggs in a large bowl. Add salt, pepper, milk, hash browns, ham, vegetables and 1 1/2 cups of cheese. Mix to combine.
Oil a 9" x 13" baking dish with cooking spray, then add egg mixture.
Top with the remaining 1/2 cup cheese.
Bake for 35-40 minutes until the eggs have set.
Slice into squares and serve.