Remove beards on mussels, and scrub shells with a brush. Discard opened, cracked, or heavy mussels (they're filled with sand). Set aside.
Heat oil in a large Dutch oven over medium heat. Add green onions and next 3 ingredients; saute until tender. Add chicken broth and next 3 ingredients; bring to a boil. Add rice; cover, reduce heat, and simmer 20 minutes. Stir in parsley; place mussels on rice. Cover and cook 8 minutes or until mussels are open. (Discard any mussels that do not open during cooking.)