Place one rack in the center of the oven and one in the upper third. Preheat the oven to 375 degrees F.

In a large ovenproof skillet, heat 1 tablespoon of the olive oil over medium heat. Add the squash, 1/2 teaspoon salt, 1/4 teaspoon pepper, basil, and parsley. Stir to coat, then add in 1/3 cup water. Cover and cook until the squash is softened, about 15 minutes.

Once the squash cubes are completely tender, remove them to a large mixing bowl (a large spoon works well for this). Discard any water that remains in the bottom of the pan. With a fork or potato masher, mash the squash well. Stir in the pasta sauce.

Heat the remaining 1 tablespoon olive oil in the same skillet over medium-high heat. Add the sausage, remaining 1/2 teaspoon salt, and remaining 1/4 teaspoon black pepper. Cook, breaking apart the meat so that it is in small bits. Cook until golden and cooked through, about 4 minutes.

Add the spinach to the sausage and break it apart so that it is mixed up with the meat. Let cook until any remaining liquid has evaporated (this should only take a minute or two), then remove the skillet from the heat. Transfer the sausage-spinach to a second large bowl and set aside. Stir in the ricotta and 1/4 cup Parmesan.

Lightly coat the skillet with nonstick spray or drizzle with a bit of additional olive oil.

Assemble the lasagna in the skillet: Spread 1 cup of the squash-marinara mixture back into the bottom of the skillet (it will be very thick). Cover with 2 lasagna noodles. Next, spread half of the sausage-ricotta mixture on top of the noodles, then sprinkle with 1/3 cup of the fontina. Add another layer of 2 noodles, the remaining sausage-ricotta mixture, half of the remaining squash-marinara mixture, and the next 1/3 cup remaining fontina. Top with the remaining 2 noodles, then the remaining squash-marinara and fontina. Sprinkle with the remaining 1/4 cup Parmesan.

Cover the skillet with a lid or piece of aluminum foil. Bake in the center of the oven for 20 minutes, then uncover and continue baking until the sauce is hot and the pasta is tender, about 5 to 10 additional minutes. Check at the 10-minute mark. If the edges seem dry, drizzle 1/4 cup water around the edges of the skillet, then re-cover and continue baking as directed.

Turn the oven to broil and transfer the uncovered lasagna to the rack in the upper third of the oven. Broil until the cheese is extra bubbly and lightly browned, about 2 minutes. Watch it carefully and do not walk away so that it doesn't burn. Let rest 5 minutes before serving.