Step 1

Place racks in upper and lower thirds of oven; preheat to 400°. Butter a 13x9" baking dish and arrange squash in dish. Heat 2 Tbsp. butter in a large high-sided skillet over medium. Add onion, garlic, and ½ tsp. salt and cook, stirring often, until onion is softened and starting to turn golden brown, 8–10 minutes. Stir in kale, red pepper flakes, and 1 Tbsp. thyme and cook, stirring, 1 minute. Using tongs, scatter onion mixture over squash, making sure to get it into all the crevices.

Step 2

Combine cream, three quarters of Parmesan, and 1½ tsp. kosher salt in skillet (no need to wipe out) and cook, stirring, until hot but not simmering, about 3 minutes. Carefully pour over squash, using tongs to turn squash to coat evenly. Cover tightly with foil, transfer to lower rack of oven, and bake until squash is just shy of tender, 25–30 minutes. Remove foil and continue to cook until cream is thickened and no longer liquid-y and squash is very tender, 18–22 minutes.

Step 3

Meanwhile, wipe out skillet and melt remaining 3 Tbsp. butter in skillet over medium heat. Add bread and remaining ¼ tsp. salt; toss to coat. Transfer to top rack in oven and bake, stirring once or twice, until golden brown and crisp, 14–16 minutes. Let cool.

Step 4

Heat broiler. Scatter breadcrumbs over gratin, crushing into smaller pieces as you go, then top with remaining Parmesan. Transfer gratin to top rack and broil until bubbling and browned at the edges, about 3 minutes. Top with a few thyme sprigs to serve.