Heat the oil in a 4-quart saucepan over medium heat. Add the onion and cook for 3 minutes, stirring occasionally.
Stir the rice in the saucepan. Add 1/2 cup broth and cook and stir until it's absorbed. Add the remaining broth, 1/2 cup at a time, stirring until the broth is absorbed before adding more. Stir in the cheese before serving.