Remove beards on mussels, and scrub shells with a brush. Discard any opened or cracked mussels.
Melt butter in a large saucepan; add shallots and garlic. Sauté 3 minutes or until translucent. Add wine; bring to a boil. Add mussels; cover and cook 5 minutes, shaking saucepan occasionally. Remove mussels with a slotted spoon when they open, discarding any that remain closed; set aside.
Add fish stock and next 6 ingredients to saucepan; simmer, uncovered, 15 minutes over medium heat. Strain, separately reserving both cooking liquid and vegetables. Discard bay leaf.
Add saffron to 1 tablespoon warm water; cover and steep 2 minutes.
Heat cream in a saucepan over medium heat until very warm (do not boil). Add saffron mixture to cream. Stir in reserved cooking liquid, salt, and pepper.
Remove half of mussels from shells. Spoon vegetables evenly into shallow serving bowls. Place 3 shelled mussels and 3 unshelled mussels on top of vegetables. Ladle warm broth over vegetables and mussels. Serve immediately.