In a medium saucepan, combine 1 3/4 cups of the chicken broth with the rice and bring to a simmer. Cover and cook over low heat for 18 minutes, until the rice is tender.
Meanwhile, in a soup pot, heat the oil. Add the kielbasa and cook over moderately high heat until lightly browned, about 4 minutes. Add the onion and cabbage and cook until softened, about 6 minutes. Add the remaining 6 cups of broth and bring to a simmer. Cook over moderately low heat until the cabbage is tender, 10 minutes. Season with salt and pepper, stir in the rice and serve.