Tap the mussels against a hard surface and discard any that do not close.
Heat the oil in a pan and gently fry the onions and garlic for 3-4 minutes, or until softened. Pour in the white wine and bring to a simmer, then add the mussels and cover with a lid for 4-5 minutes, or until the mussels have opened. Discard any unopened mussels.
Stir in the cream and parsley and spoon into a serving bowl. Serve immediately with the bread to mop up the juices.