In a large soup pot over medium heat, cook the sliced sausage until nicely browned, stirring occasionally for about 8 to 10 minutes.
Remove the sausage from the pot, ensuring to keep the rendered fat in the pot.
Add the chicken broth, red kidney beans, Cannellini beans, and chopped potatoes to the pot. Stir well, cover, and let simmer for 15 minutes.
To prepare the kale, gently massage the leaves for a couple of minutes to tenderize them.
Incorporate the softened kale into the pot, mix it thoroughly, lower the heat to medium-low, and cook for an additional 10 minutes.
Reintroduce the browned sausage to the soup, add red wine vinegar, and season with pepper if desired. Warm the mixture for a few more minutes.
Serve the soup hot and savor the comforting flavors.