Heat oven to 400 degrees F. Butter a 2-3 quart shallow baking dish. Mix together the salt, black pepper, white pepper, and garlic powder. Peel the potatoes, or not, and slice them 1/8-inch thick (no thicker), by hand, with a mandoline, or with the slicing blade in a food processor. Do not rinse the slices. Overlap 1/3 of the sliced potatoes in baking dish, like shingles. Sprinkle with 1/3 of the salt/pepper/garlic mixture, 1/2 tsp of the dill, and 1 cup of the cheese. Repeat layering twice, using the rest of the potatoes, divided, sprinkling each layer with half the remaining salt/pepper/garlic mixture, 1/2 teaspoon dill and 1 cup of cheese..Lightly whisk together the cream, chicken stock and mustard in bowl. Stir in chopped basil and pour over the potatoes. Place the dish on a baking sheet and bake at 400 degrees F for 1 hour (or optionally at 325 degrees for 2 hours), or until most of the liquid is absorbed, the top is crusty and starting to brown, and the potatoes are tender when pierced with a fork. Let the potatoes rest for 20 to 30 minutes before serving. Makes 8 to 10 side dish servings.