In a stockpot over medium-high heat, warm the oil (or butter).
Add the carrots, onion, celery, green pepper, 2 tsp each of the parsley, and thyme, ½ tsp each of the marjoram, basil, and dill. Season generously with salt and pepper.
Saute until the veggies are crisp-tender.
Add garlic. Cook and stir a minute or two.
Stir in the remaining ingredients, Parmesan rind, and the rest of the herbs. Bring to a boil.
Reduce heat; simmer, covered, until vegetables are tender, 1 to 1 ½ hours.
Remove bay leaf and Parmesan rind. Taste and adjust seasonings.