Chop both the white and green of teh onions and saute' them gently in the butter in a deep saucepan with a lid. Add the peas and cook 1-2 minutes, stirring constantly. Add the hot broth, cover and simmer 8-10 minutes. Add rice and parsley, stir once, bring to a boil, cover, and reduce the heat toa simmer. Cook about 15 minutes. Taste for seasoning and add salt if needed. Stir in the cheese.