Melt the butter in a skillet. Add the vegetables and cook until tender but still crisp, about 3-5 minutes. Mix bread, 1 cup cheese, and ham. Add cooked vegetables to the bread, cheese, and ham mixture, incorporating evenly. Put into greased 9-by-13-inch baking dish. Mix eggs, milk and seasonings. Pour over the bread mixture. Cover and refrigerate from 12 to 24 hours. Bake at 350 degrees for 45-50 minutes. Sprinkle remaining cheese on top, and heat in the oven until melted.