Wash and peel potatoes. Slice thinly with a mandolin to measure about 4 cups. Heat 3 tablespoons butter/butter in saucepan over low heat until melted; whisk in flour, salt, pepper and dry mustard. Cook over low heat, whisking constantly, until mixture is smooth and bubbly; whisk in milk a little at a time, keeping consistency thick before adding next bit of milk. Heat to boiling again, whisking constantly. Slowly add shredded cheese a little at a time.
Arrange potatoes in greased 2 quart casserole in layers, topping each layer with equal amounts of sauce, onion and cubed ham. Dot top layer with 1 tablespoon butter. Cover and bake in 350 degree oven for 30 minutes. Uncover and bake until potatoes are tender, 60-70 minutes longer. Let stand 5-10 minutes before serving.