Soak the saffron in hot water in a small bowl. Heat the oil in a large saucepan over a medium heat. Add shallots and garlic and cook for 5 minutes or until soft, stirring all the time. Add wine and bring to the boil. Increase heat to high. Add the mussels and cook covered for 5 minutes or until mussels open, stirring occasionally. Transfer the mussels to a heatproof bowl as they open to prevent overcooking. Set aside and discard any unopened mussels.
Bring the liquid to the boil and cook for 15 minutes or until reduced to 685ml. Strain into a large saucepan. Return half of the strained shallots to the saucepan and discard the rest. Add saffron and cream, bring to the boil and stir in the mussels to heat them through.
Divide mussels among shallow serving bowls. Pour over sauce and sprinkle with chopped parsley. Serve immediately.