Heat the oil and butter in a pan and gently fry the onion and garlic for 2-3 minutes. Add the white wine and bring to a simmer. Add the mussels, cover with a tightly fitting lid and steam for 5-7 minutes, or until the mussels have opened up. Discard any mussels that have not opened. Add the saffron and parsley and mix well. Remove half of the mussels and juices to a serving bowl, and into the remaining half stir the cream, heating through until steaming.
Serve both bowls of mussels with crusty bread on the side and wedges of lemon.