Set a dutch oven at medium-low heat and cook the kielbasa for around 15 minutes. The kielbasa should be well browned and render its fat. Remove the kielbasa from the dutch oven and set aside.
Add the garlic to cook in the fat from the kielbasa for 2 minutes as you stir frequently so the garlic doesn’t burn. Stir in the beans followed by the chicken broth. Cover and cook for 45 minutes then add the potatoes. Cook for 15 more minutes.
Now, add the kale and cook until it just becomes tender but do not overcook. Stir in the vinegar and pepper.
Serve the kielbasa in 4 bowls and scoop the soup on the kielbasa.