1. Bring a pot of salted water to boil. Cook pasta until al dente, about 10 minutes or as package label directs.
2. Trim ends of zucchini and squash and, using a vegetable peeler, shave lengthwise into long ribbons. Discard seeded center and any strips of peel.
3. Warm oil and butter in a large skillet over medium heat until butter melts. Add shallot; sauté until softened, about 5 minutes. Raise heat to medium-high. Add garlic, red peppers and tomatoes; cook for 3 minutes. Add zucchini, squash, Italian seasoning, broth and 1/2 tsp. each salt and pepper; sauté 2 minutes longer. Remove from heat.
4. Drain pasta, reserving 1/2 cup cooking liquid. Toss pasta with vegetables. Stir in arugula and 1/2 cup Parmesan, adding reserved liquid 1 Tbsp. at a time to moisten, if desired. Serve, passing Parmesan on the side.