Bring 4 quarts water to a boil in a large Dutch oven. Add pasta; cook 5 minutes. Add carrots; cook 2 minutes. Add peas; cook 30 seconds. Drain and rinse with cold water; drain well.
Heat oil in a large nonstick skillet over medium-high heat. Add the green onions and garlic, and sauté for 2 minutes. Add pasta mixture, broth, pattypan squash, and zucchini, and bring to a boil. Cover, reduce heat, and simmer until thoroughly heated. Stir in arugula and remaining ingredients.