Heat olive oil in a large pot or Dutch oven over medium heat. Add onion, carrots, and celery; sauté until softened, 8–10 minutes.
Add garlic, Italian seasoning, and tomato paste (if using). Stir constantly for about 1 minute.
Pour in diced tomatoes and vegetable broth. Add bay leaf and scrape up any browned bits from the bottom of the pot.
If using potatoes, add them now. Bring to a gentle simmer and cook 15–20 minutes, until potatoes are nearly tender.
Add green beans and zucchini. Simmer 8–10 minutes, until vegetables are tender-crisp.
Stir in beans (if using) and leafy greens. Cook 3–5 minutes, until greens are wilted and beans are warmed through.
Remove bay leaf. Season with salt and pepper to taste. Finish with lemon juice or vinegar, then serve hot.