Rinse mussels in cold water and scrub clean, discard any mussels that have opened
In a large pot over medium heat, heat olive oil and cook shallots for 1 minute, add garlic clove and saffron and stir an additional minute. Add broth and lime leaves and bring to a boil, reduce to simmer when boiling.
Slowly add the mussels and cover. Remove mussels that have opened and set them aside. Check mussels every 30 seconds as to avoid over cooking. Continue until all the mussels have cooked.
Once all the mussels have cooked, increase the heat to medium and stir in the cream to thicken the sauce. Season with salt and pepper if needed.
To serve: Place the mussels in a serving dish and laddle the broth overtop . Serve hot with bread on the side, sprinkle a bit of parsley and enjoy!