Combine carrots, celery, onion, garlic, green beans, kidney beans, tomatoes, broth, Italian seasoning, crushed red pepper, 1/4 teaspoon salt, and pepper in a 6- to 8-qt. slow cooker. Cover and cook on Low for 6 to 8 hours.
Stir in zucchini, pasta, and the remaining 1/2 teaspoon salt. Cover and cook on Low until the pasta is tender, 15 to 20 minutes more. Serve immediately, topping each serving with about 1 1/2 tablespoons Parmesan.
Equipment: 6- to 8-qt. slow cooker