Heat butter in a large pot over medium heat. Add onion, carrots, green beans, and celery. Cook, stirring occasionally, for about 5 minutes.
Add minced garlic and diced potato to the pot. Cook for an additional 2 minutes, stirring frequently.
Stir in zucchini, vegetable broth, bay leaves, and diced tomatoes with their juice. Season with Italian seasoning, salt, and pepper. Bring to a boil, then reduce heat and simmer for 20-25 minutes.
Add frozen corn and peas to the pot. Continue to simmer for 5 more minutes, or until all vegetables are tender. Remove bay leaves.
Adjust seasoning with salt and pepper if needed. Serve hot with fresh parsley and croutons on top.