Roll kale leaves into tight tubes and cut crosswise into 1/4-inch strips.

Heat oil in a large, heavy saucepan over medium heat. Cook and stir kielbasa in hot oil until browned, about 5 minutes. Stir green onions in with sausage; cook until onions soften, about 3 minutes. Add kale; cook and stir until kale wilts, about 3 minutes.

Pour chicken broth over the kielbasa mixture; add beans and stir. Bring the mixture to a boil, reduce heat to low, and cook at a simmer until kale is completely tender, about 15 minutes. Season with salt and pepper and top with Parmesan cheese.