Rinse and remove the beards from the mussels. If any of the shells remain open or do not fully close when rinsing, discard them as these are dead.
Heat oil over medium heat in a large lidded saucepan. Add garlic and cook until fragrant, about 1 minute. Add marinara and mussels and cover.
Bring to a simmer and cook until mussels open on their own, about 5 minutes. Stir in cream and parsley and serve immediately as an appetizer or over pasta.