Heat 1 tablespoon of the oil in a large skillet over high heat. Add the shallots, parsley, garlic, salt, saffron, pepper, and wine, and bring to a boil, stirring. Add the mussels, reduce the heat to low, cover, and steam until the shells are open, for about 3 minutes. Discard any unopened mussels. Strain and reserve the liquid (makes about 2/3 cup liquid). Keep the mussels covered and warm.

Place the egg in a food processor, turn on the machine, and slowly drizzle in the 2/3 cup mussel cooking liquid. Slowly drizzle in the remaining 1/2 cup of oil. Process until the mixture has the texture of a thin mayonnaise. Makes 1 1/3 cups.

To serve, arrange 6 mussels in each of 4 shallow soup bowls and drizzle each serving with 1/3 cup of the sauce, making sure to get some of the sauce into all of the mussel shells. Serve immediately.