Preheat oven to 350°. Grease a 13x9-inch baking dish with butter or cooking spray; set aside.
In a large mixing bowl, whisk the eggs and milk together. Add salt, white pepper and parsley. Add the yellow cheddar cheese, 1 cup of the sharp white cheddar cheese, ham, onions and diced hash browns. Mix thoroughly.
Pour into the prepared pan and sprinkle the top with the remaining 1 cup of sharp white cheddar cheese.
Bake for about 45 minutes or until the top is golden brown.