Prepare brussel sprouts by trimming outer leaves and cutting off ends. If they are large, cut in half. Place in bowl with onions (diced about the same size as the brussel sprouts) and broccoli florets. Coat with oil, salt and pepper. Place on sheet pan and roast ( shaking pan occassionally ) for 35-40 minutes.
Sprinkle with parmesean cheese after taken out of the oven and serve hot.