Preheat oven to 350℉
Spray 9 x 13" baking dish with non-stick cooking spray.
Add the frozen potatoes, ham, and cheese to a large bowl. Toss to combine. Pour the mixture into baking dish. Note: It will look very full but the egg mixture will fill in the gaps.
In a large bowl, whisk the eggs with the milk, salt, and pepper (I use the same bowl from step 1).
Pour the egg mixture over the hash brown mixture. Pat everything down with the back of a wooden spoon.
Bake for one hour, uncovered. The center should be set and the edges should be golden brown.