Once the soup has reduced to about 3 quarts and the beans are nice and tender, make the soffritto.
First, émincé the garlic. Place a small skillet on the stove top. Add the extra-virgin olive oil, garlic and chili flakes. Slowly heat the mixture over medium-low heat. Cook just until the garlic releases its aroma and just starts to turn color. Do not let it brown or burn. Add about 1 cup of the broth to the pan and let it simmer for a couple of minutes.
Pour the soffritto into the pot and stir to combine. Simmer the soup for about 5 more minutes. Season further to taste. The soup can be served as is, or it can be finished with a variety of other ingredients.
To finish the soup, remove the tough stems from the kale and tear or cut into 1 to 2" -inch pieces. Wash and spin dry.
Either prepare the vegan sausage or cut sausage into bite size pieces. Heat a skillet over medium-high heat and add the oil. Fry the sausage until cooked through and golden on all sides. Once done, transfer the sausage to plate lined with paper towels to drain. Drain any excess oil from the pan and add the kale. Toss, season with a pinch of salt and pepper to taste and cover for about 2 minutes until it wilts and becomes tender.
To serve the soup, place a bit of kale into a warmed bowl, followed by a few pieces of sausage. Ladle the hot soup over top. Serve with some shaved Parmigiano-Reggiano and a splash of quality olive oil.
To finish the soup, remove the tough stems from the kale and tear or cut into 1 to 2" -inch pieces. Wash and spin dry. Add the kale to the soup and gently simmer until softened, about 5 to 10 minutes.
If desired, drizzle with a bit of extra-virgin olive oil and serve.