Preheat the oven to 350°F.

In a large mixing bowl, combine the butternut squash with the extra-virgin olive oil, cinnamon, thyme, bay leaf, 1 teaspoon of the salt, and 1/2 teaspoon of the pepper and toss to coat the squash. Transfer the squash to a large baking sheet and cover with aluminum foil. Bake until the squash is tender, about 30 minutes. Set the squash aside, covered, until cool. Remove and discard the thyme sprigs and bay leaf.

Heat a medium sauté pan over medium-high heat. When hot, add the olive oil, onion, fennel, apple, sausage, and marjoram and cook for 8 to 10 minutes, stirring occasionally, until the sausage has browned and the vegetables have softened. Remove from the heat, transfer to a large mixing bowl, and set aside to cool. Gently fold the squash into the vegetable-sausage mixture.

Heat the butter in a small sauté pan over medium heat. When the butter begins to bubble and brown, add 1/4 cup of the sage leaves and cook until they are brown and crisp, 1 to 1 1/2 minutes. Add the chopped hazelnuts and cook for another minute. Remove from the heat and set aside to cool.

In a separate large mixing bowl, combine the ricotta, mascarpone, heavy cream, beaten eggs, half of the mozzarella, and the remaining 1/2 teaspoon pepper and 1/2 teaspoon salt. Mix well to combine, then add the cooled brown-butter-sage-hazelnut mixture and mix thoroughly.

Increase the oven temperature to 375°F.

Assemble the lasagna: Spread half of the butternut squash mixture in the bottom of the pan, sprinkle with 1/4 cup of the Parmesan, drizzle 1/4 cup of the stock over the top, and cover with 4 pasta sheets, leaving a little space between sheets. Spread 3 cups of the ricotta cheese mixture over the pasta sheets and cover with 4 more pasta sheets. Distribute the remaining half of the butternut squash mixture over the pasta, sprinkle the top with 1/4 cup of the remaining Parmesan, and drizzle with the remaining 1/4 cup stock. Place the final 4 pasta sheets over the top and spread the remaining ricotta mixture evenly over the pasta. Top with the remaining grated mozzarella and 1/4 cup Parmesan.

Cover the lasagna tightly with a piece of buttered foil and bake, undisturbed, for 40 minutes. Remove the foil and continue to bake until the top is bubbly and golden brown, about 15 minutes more. Let the lasagna stand for 15 to 20 minutes before serving. Garnish with the remaining tablespoon of sage.