Cook Italian sausage over medium heat. Break the meat into pieces with a spoon. Remove sausage from the pot and set aside. Reserve and drippings. Add additional olive oil to the pot if needed.
Add the onion, carrot, and celery and cook stirring occasionally, until vegetables begin to soften, approximately 6 minutes.
Add the tomato paste and garlic. Stir to combine and cook until garlic is fragrant, about 30 seconds to 1 minute.
Pour in the broth, beans, and kale. Bring soup to a boil, reduce heat to medium low, and simmer until vegetables are tender, about 15 minutes.
Return the cooked sausage back to the pan and stir until heated through. Add the cider vinegar. Season with salt and pepper to taste. Garnish individual bowls with Parmesan cheese if desired.