Butternut Squash Gratin

3 tablespoons unsalted butter
1 (2-pound) butternut squash
3/4 teaspoon fine sea salt
1/2 teaspoon freshly ground black pepper
1/3 cup grated Pecorino Romano cheese
2 tablespoons fresh thyme leaves
1/2 cup heavy cream

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 and bake until squash is tender, about 45 minutes. Remove cover from baking dish and preheat broiler. Broil gratin until top is browned, about 4 minutes. Serve.