Let the oil get heated in a large wide saucepan; add in the onion; cook, stirring over medium heat for 5 minutes or until tender but not browned.
Stir in the rice until coated.
Stir in the broth and salt; heat to boiling.
Cover and cook over medium heat for about 15 minutes or until the water is absorbed and the rice is tender.
Meanwhile, put the broccoli in a vegetable steamer set over 1 inch of boiling water in a covered skillet or saucepan; steam 6-8 minutes or until tender.
When the rice is cooked, stir in the ¼ cup cheese and the butter.
Spoon into a serving bowl and top with the broccoli; sprinkle with a little extra cheese.