Add the onion, carrots, celery, potatoes, green beans, zucchini, corn, garlic, and diced tomatoes to the slow cooker.
Pour in the vegetable broth, then stir in the thyme, oregano, smoked paprika, bay leaves, salt, and black pepper.
Cover and cook on LOW for 6 to 7 hours or HIGH for 3 to 4 hours, until the vegetables are tender.
About 20 minutes before serving, stir in the frozen peas and allow them to heat through.
Remove the bay leaves and taste the soup, adjusting the seasoning if needed.
Ladle into bowls and finish with chopped parsley and grated Parmesan, if desired.