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Add the mussels and cook them for 3 to 5 minutes or until they have opened. Remove the mussels with a slotted spoon and add them to your large plate set to the side. Pour the stock through a sieve into a large bowl. Pour the stock back into the pot and return the soup to a simmer. Discard the garlic and bay leaf. Add the cream and taste the stock to check if you need to add salt and pepper to taste. Add the monkfish medallions to the stock and cook them for 1 minute. Return the mussels and vegetables to the pot and cook everything for 2 minutes or until it's all heated through. Stir the soup occasionally with a wooden spoon or a ladle. Remove the fish, mussels and vegetables from the soup with a slotted spoon and divide them evenly between each of your serving bowls. Ladle broth into each bowl and sprinkle the soup with tarragon and parsley.
This will strain the bay leaf, garlic and other food particles from the stock.