Rub an oval gratin dish or rectangular (14 x 8 inches) 2 quart gratin dish with garlic. Preheat the oven to 325 degrees.
Slice the potatoes into slices only 1/16 to 1/8-inch thick. You'll build up 3 layers in the gratin dish. Overlap the potato slices for the first layer and sprinkle with 1/2 teaspoon of salt, pepper and 1/2 of the cheese. Drizzle some cream over the top and dot with 1 tablespoons of butter. Repeat with more potatoes, cheese, cream and salt and pepper and butter. Repeat with last layer, keeping it free of cheese but dotted with butter. Pour chicken broth over the top and bake for 1 1/2 hours, basting the potatoes, in the middle of baking time, with liquid accumulated in the bottom of the gratin dish.