Preheat oven to 450°.
Arrange squash in a single layer on a jelly-roll pan coated with cooking spray. Lightly coat squash with cooking spray; sprinkle evenly with 1/4 teaspoon salt. Bake at 450° for 20 minutes or until squash is tender, stirring after 10 minutes. Cool squash slightly.
Combine 1/4 teaspoon salt, parsley, and next 5 ingredients (through garlic) in a food processor; process until finely chopped, scraping sides. With processor on, slowly pour broth through food chute, processing until well blended.
Combine the remaining 1/4 teaspoon salt, squash, pasta, and pesto in a large bowl, and toss well to coat. Add arugula, shallots, and pepper; toss to combine. Serve immediately.