How to Make It
Preheat the oven to 400°. Line a rimmed baking sheet with parchment paper. Season the squash halves generously with salt and pepper and drizzle with olive oil. Roast, cut side down, for about 1 hour, until the squash can be easily pierced with a knife. Let cool slightly and keep the oven hot.
Meanwhile, in a medium saucepan, warm 1 tablespoon of olive oil until shimmering. Add the sausage and cook over moderately high heat until browned and cooked through, about 7 minutes. Using a slotted spoon, transfer the sausage to a plate lined with paper towels and drain. Wipe out the saucepan.
In the same saucepan, warm 1 tablespoon of olive oil until shimmering. Add the onion, garlic and crushed red pepper and season with salt and pepper. Cook over moderate heat, stirring occasionally, until the onions are softened, about 5 minutes. Add the tomatoes and their juices, butter and browned sausage and simmer over moderate heat, stirring occasionally, until the sauce is thickened and flavorful, about 20 minutes. Remove the pan from the heat and stir in the 1/4 cup of basil. Season with salt and pepper. (You will have about 3 cups of meat sauce.)
Turn the roasted squash halves cut-side up on the prepared baking sheet. Spoon 1/4 cup of the meat sauce into each half. Sprinkle 2 tablespoons of the mozzarella and 1 tablespoon of the Parmigiano into each half. Spoon 1/2 cup more of the meat sauce into each squash and top each with 1/4 cup mozzarella and 2 tablespoons of Parmigiano.
Bake the squash lasagna for about 25 minutes, until the tops are browned and bubbling. Let cool for 10 to 15 minutes before serving. Sprinkle with chopped basil and the remaining 1/4 cup of the Parmigiano before serving.