Cut squash in half, separating long neck from rounded end. Using a sharp vegetable peeler, remove skin. Slice each half lengthwise, remove seeds and fibers from rounded end. Dice squash in ½ inch cubes.

Set large sauté pan onto oven floor, add butter and melt. Add shallots or onion to pan and cook for about 2 minutes.

Add squash, chopped thyme, and salt and pepper to pan and cook for 8 minutes or until squash begins to soften and brown around edges. Transfer squash to a ceramic baking dish. Set aside.

Add cream to sauté pan and bring to a simmer. Add ½ cup cheese and stir until melted. Pour sauce over squash, add thyme sprigs and sprinkle with remaining cheese. Bake for 15 minutes or until top is browned.