In a 5-quart slow cooker, combine frozen corn and/or peas, onion, carrots, zucchini, and garlic.
Stir in broth, tomato paste, salt, and basil.
Cover and cook on low-heat setting for 7 to 8 hours or on high-heat setting for 3 1/2 to 4 hours.
If using low-heat setting, turn to high-heat setting. Stir in frozen green beans and a pasta such as ziti or macaroni. Cover and cook for 45 minutes more.
Before serving, stir in parsley.