Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9x13-inch baking dish.

Season beaten eggs with pepper; pour into baking dish. In a large bowl, combine soup, sour cream, hash browns, ham, onion and cheese. Mix thoroughly and pour over eggs.

Bake uncovered for 30 minutes. Remove and drizzle butter over top of casserole. Return to oven and bake for an additional 15 minutes, until golden.