In a large bowl, whisk together the oil, basil, and half of the Parmesan. Stir in the tomatoes, and season with salt and pepper. While the squash is still warm, scrape it with a fork to form strands. Add the strands to the tomato mixture, and toss well. Place the mixture into serving bowls, sprinkle the remaining Parmesan on top, and garnish with the additional basil.