Toss kale, squash, garlic, salt and pepper together in medium bowl.
Heat cream over medium heat in small saucepan until hot but not simmering, stir in Dijon mustard and nutmeg. Layer half the squash and kale mixture into stoneware baking dish, top with half the cheese and then the remaining squash and kale. Pour the warm cream over the squash and press down gently. Cover with foil and bake for 25 minutes.
Remove foil, scatter remaining cheese over the top of the gratin and bake for an additional 15 minutes until top is browned and bubbly. Remove from oven and let sit for 10 minutes before serving.