For the dressing: combine all ingredients in a mason jar and shake until completely combined. Set aside.
Heat oven to 425 degrees F.
Toss squash with Parmesan cheese and 2 tablespoons of the dressing. Spread on a rimmed baking sheet sprayed with cooking spray. Bake for 15-20 minutes, or until tender, stirring halfway through. Set aside to cool.
Once the squash has cooled, place it in a large salad bowl with the remaining ingredients. Add remaining dressing and toss gently.