Heat 2 tablespoons of olive oil in your stockpot over medium heat. Add the finely chopped onion and cook until soft and translucent, about 5 minutes. Stir in the chopped fresh thyme and minced garlic, cooking for another minute until fragrant.
Toss in the chopped cabbage, celery, and carrots. Stir well to coat the vegetables with the aromatic base. Let them cook for about 5 minutes, stirring occasionally, to soften slightly.
Pour in the 10 cups of chicken broth, then add the diced potatoes and Parmesan cheese rind if using. Bring everything to a gentle boil, then reduce to a simmer. Cover and cook for about 20 minutes until the potatoes and other vegetables are tender.
Stir in the rinsed cannellini beans, canned chopped tomatoes with juices, chopped kale or spinach, and zucchini. Season with 1 teaspoon salt and 1 teaspoon granulated white sugar. Simmer uncovered for another 10-15 minutes, allowing the flavors to meld and the greens to wilt.
Remove the Parmesan rind (if used). Stir in the grated Parmesan cheese and chopped fresh basil. Taste and adjust seasoning with freshly ground black pepper and additional salt if needed.
Serve the soup hot with a drizzle of olive oil on top if desired. This soup pairs wonderfully with crusty bread or a light salad for a complete meal.