Cook the sausage in a big, deep, nonstick skillet with olive oil, breaking it up with a wooden spoon until it's done, about 5 minutes. Simmer the garlic and onions for two minutes, or until they are tender. To taste, add the tomatoes, basil, salt, and black pepper. Simmer for 15 to 20 minutes on low, covered.
In the meantime, use a sharp knife, a mandolin (be careful), or a high-quality spiralizer to slice the butternut squash into 1/8-inch thick rounds. Refer to the notes.
Turn the oven on to 375°F.
Mix the Parmesan cheese, ricotta cheese, egg, and parsley in a medium-sized bowl.
Spread 3/4 cup of sauce on the bottom of a deep 9-by-12 casserole dish, then arrange 12 rounds of butternut slices on top. Cover with 3/4 cup of the ricotta cheese mixture, then 1 cup of the sauce and 1 cup of mozzarella cheese. Layer 2: Arrange 12 additional butternut rounds, 3/4 cup of ricotta mixture, 1 cup of mozzarella, and 1 cup of sauce. Layer 3: 12 butternut slices, 1 1/2 cups sauce, and a foil-covered top.
Bake for thirty minutes with a cover on.
Take off the foil and cook for 30 minutes without a cover to help remove any extra moisture. After adding the remaining cheese on top, bake for 5 minutes, or until the cheese is melted and bubbling.
Before serving, let stand for 5 to 10 minutes. Cut into eight pieces.
Lasagna with butternut squash