Preheat oven to 350 degrees. In a large skillet melt 2 tablespoons of butter over medium heat. Saute onions, bell peppers, and ham until the onions are clear, and ham has browned. In a large bowl, combine hash browns sauteed ham and vegetables and 1 can on condensed soup. Stir until hash browns are coated.
Pour potatoes into a 9 x 13-inch pan that has been sprayed with non-stick spray. Sprinkle half of the cheese over the casserole and cover with foil. Bake for approximately 45 minutes, remove foil, add the remaining cheese and return to the oven, and cook for an additional 15 minutes. The cheese should begin to brown when the casserole is ready.