Kielbasa Cajun Dirty Rice

Heat oil in a wide 5 to 6-quart heavy pot over moderate heat until it shimmers, then brown sausage in 2 batches, turning, about 3 minutes per batch. Transfer sausage as browned to a bowl. Cook onion, bell pepper, and celery in fat remaining in pot over moderately low heat, stirring occasionally, until pepper is softened, about 6 minutes. Add garlic and cayenne and cook, stirring, 1 minute. Add broth and water and bring to a boil. Stir in rice and bring to a rolling boil. Cover rice, then reduce heat and cook over low heat, undisturbed, until liquid is absorbed and rice is tender, 15 minutes. Remove from heat and let stand 5 minutes, covered.