Preheat your oven to 375°F. Grease a 9x13-inch baking dish.
In a large mixing bowl, combine the thawed hash browns, diced ham, cream of potato soup, sour cream, and 1 1/2 cups of the shredded cheddar cheese. Stir until all ingredients are well mixed.
Transfer the mixture to the prepared baking dish, spreading it out evenly.
Sprinkle the top with the remaining 1/2 cup of shredded cheddar cheese and the grated Parmesan cheese.
Bake in the preheated oven for about 1 hour, or until the casserole is bubbly and the top is golden brown.
Let the casserole stand for a few minutes before serving to allow it to set.