Prepare vegetables: Chop onion, carrots, celery, zucchini, and green beans; mince garlic.
Add ingredients to slow cooker: Combine onion, garlic, carrots, celery, zucchini, green beans, diced tomatoes, beans, broth, olive oil, oregano, basil, thyme, red pepper flakes, salt, and pepper.
Slow cook: Cover and cook on low for 6–7 hours or high for 3–4 hours, until vegetables are tender.
Add pasta: About 20–25 minutes before serving, stir in pasta and cook until tender.
Add greens (optional): Stir in spinach or kale during the last 5–10 minutes of cooking.
Serve: Ladle soup into bowls and garnish with fresh parsley and grated Parmesan cheese.