Preheat oven to 450 degrees F. Place garlic in an ovenproof ramekin, and drizzle with olive oil. Roast until light brown and very soft, about 20 minutes. Let stand until cool enough to handle; peel garlic and cut into slivers; set aside. Lower oven temperature to 400 degrees F.
Peel squash, halve lengthwise, and seed. Cut crosswise into 1/4-inch-thick slices; set aside.
Place the kale in a steamer basket over boiling water, cover, and steam until bright green and wilted, 2 to 3 minutes. Remove from heat and roughly chop. Squeeze out as much water as possible; set kale aside.
Butter a 2 1/2-quart gratin dish. Distribute half the sliced squash in the dish, reserving the prettiest slices for the top layer. In a small bowl, combine the butter nutmeg, salt, and pepper. Distribute half the sliced garlic over squash, and sprinkle with 1/3 of seasoning mixture and 1 teaspoon thyme.
Arrange the kale over squash, and sprinkle with 1/3 of the seasoning. Arrange remaining squash over kale, and sprinkle with remaining seasoning and 1 teaspoon thyme. Distribute remaining garlic over squash, tucking it between slices.
Pour cream over assembled gratin, and cover with a piece of parchment. Bake until squash is soft when pierced with the tip of a knife, 40 to 45 minutes; halfway through the baking time, remove parchment, press down on squash with a spatula to compress and distribute the liquid; cover and continue baking. Meanwhile, combine bread crumbs, Parmesan, 1/2 teaspoon salt, and 1/4 teaspoon pepper. After 45 minutes, lower oven temperature to 375 degrees F, and remove the parchment paper. (If you're planning to reheat this dish later, let cool, and transfer to refrigerator.) Sprinkle the bread crumb mixture over the squash; return to oven and continue to bake, uncovered, until golden brown, about 10 to 15 minutes. Transfer to a wire rack to cool for 15 minutes. Garnish with remaining thyme.
To reheat: Do not add final layer of bread crumb mixture. Remove from the refrigerator, and let come to room temperature, 15 to 20 minutes. Cover with parchment paper, and reheat in a 400 degrees oven for 20 minutes. Top with bread crumb mixture and bake until golden brown, about 10 to 15 minutes. Garnish with thyme.