Add all remaining ingredients up through the Parmesan rind (if you have one on hand), and bring the soup to a boil. Cover and reduce the heat to low, then simmer for 1 hour, stirring occasionally, until all of the veggies are tender.
28 ounces diced tomatoes, 15 ounces white navy, cannellini, or great northern beans, 15 ounces red kidney or pinto beans, 2 stalks celery, 2 large carrots, 2 small zucchini, 4 cups water, 2 cups beef broth, 2 teaspoons dried basil, 1 teaspoon sugar, 1 teaspoon oregano, 1 teaspoon Kosher salt, ½ teaspoon dried thyme, ½ teaspoon dried rosemary, ½ teaspoon black pepper, ¼ teaspoon red pepper flakes, 2 bay leaves