In a large skillet, heat 1 tablespoon of extra virgin olive oil over medium heat. Add the sausage, breaking it apart, and cook for about 5 minutes until browned. Stir in the chopped onion and minced garlic, cooking for an additional 2 minutes until softened. Add crushed tomatoes and basil, seasoning with salt and pepper. Let simmer for 15-20 minutes until thickened.

Use a mandoline or sharp knife to slice the butternut squash into 1/8-inch rounds, creating the no-noodle layers. Set slices aside while preparing the cheese mixture.

In a mixing bowl, blend ricotta, Parmigiano Reggiano, and parsley until creamy. Add the egg to bind the mixture and mix thoroughly.

In a greased 9x12 casserole dish, layer meat sauce, half butternut squash rounds, half ricotta mixture, and 1 cup of mozzarella. Repeat layers with remaining ingredients, finishing with meat sauce.

Preheat oven to 375°F (190°C). Cover casserole with foil and bake for 30 minutes, then remove foil to brown the top for another 30 minutes until cheese is bubbly and golden.

Let the lasagna cool for 5-10 minutes before slicing into 8 pieces. Serve warm.