Peel the potatoes and shred them in a food processor or grate them by hand. They will quickly turn brown. You can keep that from happening by putting them in a bowl and adding about ½ tsp. cream of tartar to enough water to cover the potatoes. Swish them around a bit and then drain.
Mix the potatoes and ham together in a bowl.
In a separate bowl, combine the salad dressing, yogurt, and mayonnaise. Add this to the potatoes and ham and stir well to coat.
Put it all into a greased rectangular baking dish.
Bake at 350 degrees for 30 minutes, cover the dish with foil and cook another 15 minutes.
Check the potatoes for doneness, sprinkle the cheese over top and return the dish to the oven for a few minutes to melt the cheese.
Recipe by Gluten-Free Homemaker at http://glutenfreehomemaker.com/ham-potato-casserole-whats-for-dinner/