Preheat oven to 350°F. Butter a 9-inch baking dish with 1 tablespoon butter. Peel and seed squash, then thinly slice using a hand slicer, such as a Benriner or Mandoline slicer. Layer squash in baking dish, sprinkling some of salt and pepper between each layer. When baking dish is half filled, sprinkle 1/2 of cheese and thyme over squash. Continue layering squash with salt and pepper. Pour cream evenly over top layer, then sprinkle with remaining cheese and thyme. Cover baking dish with foil and bake until squash is tender, about 45 minutes. Remove foil from baking dish and preheat broiler. Broil gratin until top is browned about 4 minutes. Serve.
Chef Thomas Keller, author of Ad Hoc at Home, explains how to season food with salt and vinegar, and why you should temper your food.