In a covered Dutch oven over medium-high heat, cook oysters with white wine, garlic, and herbs. Bring liquid to a simmer and steam until shells open.
Remove mussels from pot. Add cream, salt, and pepper to pot; simmer, uncovered, until mixture coats the back of a spoon.
To serve, pour equal portions of sauce into soup bowls. Arrange mussels on top; garnish with parsley.