Preheat oven to 400°F. On a baking sheet, toss together the olive oil, butternut squash, garlic, shallot, sage, rosemary, salt, and pepper. Bake for 20 minutes, until the squash is tender.
Add the roasted butternut squash, garlic, and shallot to a food processor. Puree until smooth. Add 1/3 cup heavy cream and 1/3 cup parmesan. Season with salt and pepper. Blend until creamy.
Meanwhile, drain 3 tablespoons of oil from the sun-dried tomato jar into a large pot or skillet with sides. Chop the sun-dried tomatoes and set aside.
Set the pot over medium-high heat. Add the chicken, 2 tablespoons of Italian seasoning, salt, and pepper. Cook until golden brown, about 5 minutes. Remove the chicken from the pot.
To the same pot, add the butter and 1 tablespoon Italian seasoning. Cook until fragrant, about 1 minute. Add 3 1/2 cups water. Bring to a boil, add the pasta, and cook, stirring often, until the pasta is al dente, about 8 minutes.
Stir in the butternut puree, 2/3 cup heavy cream, 2/3 cup parmesan, chopped sun-dried tomatoes, and the cooked chicken with any juices left on the plate.
Serve topped with parmesan and fresh basil. Enjoy immediately.