Heat the oil in a large pot over medium high heat. Add the onion, carrot, and celery. Sauté the vegetables, stirring every minute or so, for 5-7 minutes, or until the onion is translucent and the carrot is tender.
Add the garlic and tomato paste to the pot. Cook, stirring constantly, for another minute, or until the garlic is quite fragrant.
Add the tomatoes, beans, broth, water, salt, and pasta to the pot. Bring to a rapid simmer. Reduce the heat to low, cover, and simmer the soup for 15-20 minutes, or until the pasta is cooked through. I like this to be a thicker soup, but if the soup is too thick for your liking, and an additional 1-2 cups water.
Add the chopped greens and cashew parmesan to the pot. Recover and simmer for 8-10 minutes, or until the kale is tender.
Taste the soup. Add a splash of vinegar, if you like, plus any additional salt you'd like and freshly ground black pepper to taste. Serve the soup with an extra sprinkle of cashew parmesan and some toast, focaccia, or a green salad. Enjoy!