Melt the butter in a large pan and soften the shallots. Pour over the wine and let it bubble up before adding the mussels.
Cover and cook over a high heat, shaking, until the mussels open.
Place a colander over a bowl and strain the mussels, reserving the liquid. Discard any mussels that have not opened. Remove the mussels from their shells and reserve, discarding the shells.
Strain the reserved liquid into a pan and add the fish stock. Bring to a simmer, stir in the saffron and remove from the heat.
Carefully whisk in the egg and cream liaison then return to the heat and warm through without boiling. Add the mussels.
When the soup has thickened check the seasoning then pour into bowls and sprinkle with parsley. Serve with the bread.