Warm the pot: Heat 1–2 tablespoons of olive oil in a large pot over medium heat.
Sauté aromatics: Add onion, celery, and carrots (if using). Cook 5–7 minutes, stirring, until the onion softens. Add garlic and cook 30 seconds until fragrant.
Build the base: Stir in tomato paste and cook 1 minute to caramelize slightly.
Add diced tomatoes with their juices and stir.
Add vegetables: Stir in zucchini, green beans, and cauliflower florets. Season with 1 teaspoon salt, black pepper, and Italian seasoning. Add a pinch of red pepper flakes if you like heat.
Pour in broth: Add 6 cups broth.
Drop in the bay leaf and Parmesan rind if using. Bring to a gentle boil, then reduce to a simmer.
Simmer: Cook uncovered 15–20 minutes, or until vegetables are tender but not mushy. Stir occasionally.
Add greens and beans: Stir in spinach or kale and the beans if using.
Simmer 3–5 minutes more, until greens wilt.
Finish and taste: Remove bay leaf and Parmesan rind. Add a squeeze of lemon juice or a splash of vinegar. Taste and adjust salt and pepper.
Serve: Ladle into bowls and top with chopped parsley or basil.
Add grated Parmesan if desired.