Preheat oven to 425°F.
Trim squash ends and cut the squash crosswise into 4 equal rounds. Scoop out the seeds and discard. Place the rounds on a rimmed baking sheet; drizzle with 2 tablespoons oil and sprinkle with 1/4 teaspoon pepper and 1/8 teaspoon salt.
Combine mushrooms, tomatoes, sausage, the remaining 1 tablespoon oil, 1/4 teaspoon pepper and 1/8 teaspoon salt in a medium bowl. Spread in an even layer around the squash.
Roast until the squash is tender, 30 to 40 minutes.
With a fork, shred the squash in the center of the rings into long strands. Divide the mushrooms, tomatoes and sausage among the squash nests. Drizzle with vinegar and sprinkle with Parmesan and basil.