Step 1

Preheat the oven to 400°F. On a large rimmed baking sheet, toss together the butternut squash, sage leaves, 3 tablespoons olive oil, 1 1/2 teaspoons salt, and 1 teaspoon pepper. Spread into an even layer and roast until the squash is tender, about 45 minutes.

Step 2

Meanwhile, heat a large skillet over medium heat. Add the Italian sausage and cook, stirring occasionally to crumble into small pieces, until the sausage is browned and cooked through, about 8 minutes. Remove from the heat and set aside.

Step 3

Transfer the roasted squash and sage to a food processor with the half-and-half. Puree until the mixture is smooth and creamy, about 1 minute, stopping to scrape down the sides of the bowl as needed. Set aside.

Step 4

Wrap the spinach in a double layer of paper towels and squeeze to remove as much liquid as possible. In a large bowl, stir together the spinach, cottage cheese, eggs, ½ cup parmesan, garlic, 1 teaspoon salt, and the remaining ½ teaspoon pepper. Set aside.

Step 5

Bring a large pot of water to a boil over medium-high heat. Add the remaining 1 tablespoon olive oil and ½ teaspoon salt to the boiling water, and cook the lasagna noodles until al dente, about 8 minutes. Drain and lay flat on a lightly greased baking sheet.

Step 6

To assemble: Arrange 4 cooked lasagna noodles in the bottom of a 13-by-9-inch baking pan, overlapping slightly if necessary. Spoon one third of the squash puree over the noodles; spread evenly. Top with half of the whole milk mozzarella slices (about 5 slices). Sprinkle evenly with half of the Italian sausage. Spoon half of the cottage cheese mixture over top; spread evenly. Repeat the layers with the noodles, squash puree, whole milk mozzarella slices, Italian sausage, and cottage cheese mixture. Top with the remaining 4 noodles and squash puree, spread evenly. Top with fresh mozzarella and sprinkle with the remaining 1/4 cup parmesan.

Step 7

Cover the lasagna tightly with foil. Bake at 400°F for 30 minutes. Uncover, and continue baking until the lasagna is heated through and the top has browned, 20 to 25 minutes. Let stand for 10 minutes before serving with more parmesan.