Preheat the oven to 400 degrees. Use butter to lightly grease a large (2 1/2-quart) gratin dish.
Peel the squash, then cut it crosswise into 1/4-inch-thick slices.
Heat the oil in a large skillet over medium-high heat. Add the kale, still slightly damp, and cook, stirring occasionally, for about 3 minutes, until it has wilted. Add the garlic and cook, stirring, for 45 to 60 seconds, until it is fragrant.
Place half of the sliced squash in the prepared gratin dish; season with salt and pepper to taste.
Combine the nutmeg, allspice and thyme in a small bowl.
Place the kale over the squash and sprinkle with half of the nutmeg-thyme mixture. Top with the remaining squash and sprinkle with the remaining nutmeg-thyme mixture.
Pour the cream over the vegetables; cover the gratin dish tightly with aluminum foil. Bake for about 45 minutes, until tender.
While the vegetables are baking, combine the panko bread crumbs and Parmigiano-Reggiano cheese in a small bowl.
Reduce the oven temperature to 375 degrees. Discard the foil from the gratin dish and use a spatula to press down on the mixture. Sprinkle the bread crumb-cheese mixture over the vegetables. Return to the oven and bake, uncovered, for about 10 minutes, until golden brown. Transfer to a wire rack to cool for at least 10 minutes before serving.
It's best to buy kale just before you are going to use it, because it tends to get flabby and bitter after a few days' refrigeration. Store it in an open plastic bag in the coldest part of the fridge.