In a large covered saucepan over medium heat, steam mussels and green onions in wine until mussels open. Discard any unopened mussels.
Remove pan from heat and drain liquid into a skillet set on medium heat.
Stir in cream and vegetables; simmer until liquid is reduced by half.
Stir in Hollandaise Sauce; blend well.
Place 12 mussels in each of 4 serving dishes. Top with sauce and sprinkle with parsley.