Brown the sausage. Heat 1 ½ tablespoons of olive oil over medium-high heat in a large, heavy-bottomed soup pot or Dutch oven. Add the sausage and saute until cooked through and nicely caramelized, breaking it apart with a wooden spoon as you go. Use a slotted spoon to transfer the cooked sausage to a bowl. Set aside.
Saute the veggies. Add the remaining olive oil to the pot, followed by the onion, carrot, celery, and garlic. Season with salt, pepper, and Italian seasoning. Saute until the veggies have softened. Add the kale and saute until it has wilted substantially. If the veggies start to burn, add a splash of chicken stock.
Make it soup. Stir the chicken stock, cannellini beans, and cooked Italian sausage.
Simmer. Bring the soup to a boil and then reduce the heat to low. Simmer for 15 minutes.
Season. Taste the soup and season with salt and pepper to taste.
Notes
If you prefer your soup to be a bit thicker, you can make a cornstarch slurry with a 1 to 1 tablespoon ratio of cornstarch and water. Add as much as needed, letting it cook for a few minutes over low heat until you get the creamy texture you are looking for. You could also use less chicken broth or stock for a more chili-like texture.