Scrub and debeard mussels. In a large kettle, combine parsley, white wine, and shallots, and bring to a boil. Steam the mussels in the boiling liquid until opened. Drain and save the cooking stock. Remove only top shells of mussels and discard.
Arrange mussels in ovenproof serving casserole. Strain cooking liquid through cheese cloth. Pour in a saucepan and bring to a boil.
In a small saucepan, melt butter, and add flour to make roux. Stir roux in stock and whisk to thicken. Add the saffron. Pour a little sauce into egg yolks. Mix well and stir into remaining sauce.
Heat sauce but do not boil. Season to taste with salt, pepper.
Do not add salt since the mussel stock is salty. Pour sauce over the hot mussels. Serve immediately.