Preheat oven to 400℉.
Butter the bottom and sides of a gratin pan with 1 Tablespoon of butter. (Any 2 ½- to 3-quart gratin dish or other shallow baking dish.)
In a small bowl combine the salt, pepper, garlic powder and dry mustard and set aside.
Peel potatoes and thinly slice with a mandolin, food slicer, food processor or carefully with a knife. The slices should be about ⅛ inch. So that the potatoes don't turn brown, I usually keep the whole, peeled potatoes in a bowl of water and dry each one with a clean towel before slicing.
Place ⅓ of the sliced potatoes in the bottom of the buttered pan overlapping each other.
Sprinkle ⅓ of the seasoning mixture on the sliced potatoes.
Sprinkle ⅓ of the cheese on top of the seasoned potatoes.
Do this again - ⅓ potatoes, ⅓ seasoning and then ⅓ of the cheese.
Place the remainder of the potatoes in the dish and sprinkle with the remainder of the seasoning (do not add the cheese yet).
In a separate bowl combine the broth and the heavy cream and pour evenly over the potatoes.
Sprinkle the remaining cheese on top.
Dot the top of the gratin with 2 Tablespoons of butter.
Cover the dish tightly with foil and bake for 30 minutes.
Uncover and continue to bake for 30 minutes longer or until the potatoes are tender and the gratin is golden brown on top.
Let the gratin sit for 10 minutes before serving.