Preheat the oven to 400°F. Butter a large gratin dish. Peel the squash, then cut crosswise into 1/4-inch slices; set aside.

Bring a large pot of salted water to a rolling boil. Add the kale and cook until just tender, about 5 minutes. Drain well in a colander, then squeeze out any excess water.

Heat the oil in a large sauté pan over medium-high heat. Add the garlic and the well-drained greens. Cook until the greens are slightly wilted, 3 to 4 minutes. Taste and adjust for seasoning with salt and pepper.

Meanwhile, place half the sliced squash in the prepared dish and season with salt and pepper. Combine the nutmeg, allspice, and thyme in a small bowl. Spoon the kale over the squash and sprinkle with half the seasoning mixture. Top with remaining squash and sprinkle with the remaining seasoning.

Pour the cream over the gratin and cover with a piece of aluminum foil. Bake for 25 minutes, remove the foil, and press down on the squash with a spatula to compress. Cover and continue baking until the squash is soft when pierced with the tip of a knife, about 20 minutes.

Meanwhile, combine the breadcrumbs and cheese in a small bowl. Season with salt and pepper. Decrease the oven temperature to 375°F. Remove the foil from the gratin dish and sprinkle the breadcrumb mixture over the squash. Dot with the butter and continue baking, uncovered, until golden brown, about 10 minutes. Transfer to a wire rack to cool for about 10 minutes before serving.