Heat a large pot or Dutch oven over medium heat. Add the Italian sausage and cook, breaking it up, until browned and fully cooked. Transfer the sausage to a plate and set aside. In the same pot, add olive oil, onion, celery, and carrots. Cook for about 5 minutes, stirring occasionally, until the vegetables begin to soften.
Add the grated garlic and cook for 1 minute, stirring constantly, until fragrant.
Pour in the chicken broth, tomato sauce, and water. Bring to a boil, then reduce heat to a gentle simmer. Cover and simmer for 15 minutes, or until the vegetables are tender.
Stir in the cooked sausage, kale, cannellini beans, kidney beans, Italian seasoning, and pasta. Bring back to a boil, then reduce heat, cover, and simmer for 12 to 15 minutes, stirring frequently, until the pasta is al dente. Finish the soup with red wine vinegar, then season with salt and black pepper to taste. Serve hot with freshly grated parmesan cheese.
