The Best Squash Lasagna

Ingredients

• 1 large kabocha squash or sugar pumpkin, quartered, seeds discarded
• 1 tablespoon olive oil
• Kosher salt and freshly ground black pepper
• 1 large egg
• 4 ounces cream cheese
• 6 tablespoons unsalted butter, divided
• 2 tablespoons maple syrup
• 1/4 teaspoon cinnamon
• 1/4 teaspoon freshly grated nutmeg, divided
• 2 crisp baking apples such as Golden Delicious, peeled, cored, and cut into 1/2-inch dice
• 1/4 cup minced fresh sage leaves
• 1 package no-boil lasagna noodles
• 2 medium cloves garlic, minced
• 2 tablespoons flour
• 2 cups whole milk
• 12 ounces shredded Gruyère cheese

Directions

1. Set a rack in the center of the oven and heat it to 325 degrees F. Rub three squash quarters all over with 1 tablespoon olive oil, using your hands to coat them well. Sprinkle with salt and pepper. Set them in a cast iron skillet, or use a foil-lined rimmed baking sheet, and roast for about 45 minutes, until a knife slides easily into the flesh near the stem. Take the squash out and let it sit until you can handle it comfortably. Turn the oven up to 400 degrees F.
2. Scoop the flesh from the roasted squash into the bowl of a food processor. Add the egg and cream cheese, then drop in 2 tablespoons butter. Pour in the maple syrup, followed by the cinnamon and half of nutmeg. Run the machine until the mixture is completely smooth. Move the purée to a medium bowl and keep it nearby.
3. While the squash is roasting, dice the remaining squash quarter into 1/2-inch pieces. In a large skillet over high heat, melt 2 more tablespoons butter; move the pan around until the foam settles down. Stir in the diced squash and apple, then cook for about 10 minutes, tossing and stirring often, until they have softened and picked up color across most surfaces. Taste and season with salt and pepper, then stir in the minced sage. Spoon the mixture into a bowl and set it aside.
4. Lay the lasagna noodles in a 9- by 13-inch casserole dish, then pour in enough cold water to cover them. Let them sit, swishing them around now and then so they do not cling together.
5. As the noodles soak, put the remaining 2 tablespoons butter and the garlic into a medium saucepan set over medium heat. Stir as it cooks; after about 1 minute, the butter should be melted and the garlic should smell fragrant. Sprinkle in the flour and whisk for about 2 minutes, just until it turns pale blond and takes on a nutty scent. Keep the whisk moving while you pour in the milk slowly, in a thin, steady stream. When the milk has all gone in, let the sauce reach a boil, give it a strong whisk, and take the pan off the heat. Whisk in 8 ounces of Gruyère cheese until the sauce is smooth all the way through. If you still see lumps, smooth it out with a hand blender, or use a standing blender. Stir in the remaining 1/8th teaspoon nutmeg, then add salt and pepper to taste. Keep the sauce aside.
6. Lift the lasagna noodles out of the baking dish and lay them on clean dish towels, letting the towels take up the extra water.
7. Coat the bottom of the baking dish with 1/6th of the white sauce, then lay three lasagna noodles over it. Spoon on 1/5 of the squash purée, followed by 1/4 of the sautéed squash and apple mixture. Drizzle another 1/6th of white sauce on top. Build 3 more layers the same way, using noodles, squash purée, cooked squash mixture, and white sauce in that order. By now, the sautéed squash should be gone, with 1/6th of the white sauce and 1/5th of the squash purée still waiting. Add the final three noodles. Cover them with the purée that is left, then scatter the remaining 4 ounces of shredded Gruyère over that. Finish by drizzling on the last of the white sauce. Cover the dish with aluminum foil and put it in the oven.
8. Bake it under the foil for 20 minutes. Uncover the dish, then bake for about 15 minutes longer, until the top is browned and bubbling. Take it out of the oven, give it 5 minutes to settle, then slice and serve.