Simple Potato Gratin

Name: Simple Potato Gratin
Ingredients: 3 tablespoons butter, cut into pieces, plus an additional pat for buttering gratin dish; 4 large yellow potatoes* (about 1 1/2 pounds), peeled; Salt and freshly ground black pepper; 1 cup milk, half-and-half or cream (if using something richer than milk, you can skip the butter); 2 ounces cheese, grated or crumbled (Parmesan or Gruyere are the classics, but that doesn't mean that goat cheese, blue cheese or any of your favorites won't work as well) [optional]