In a large heavy bottomed pan melt the butter and add the olive oil. Add the onion, celery, garlic, and thyme and sauté for at least ten minutes to soften them, without colouring.
Turn up the heat and add the wine, Pastis and a good few turns of the pepper mill. Bring to a simmer. Then tip in the mussels and cover with tight-fitting lid.
Steam the mussels for five minutes shaking the pan occasionally until the mussels are all open. Remove from the heat.
Squeeze in the lemon juice and stir in the parsley, stir and serve with lots of crusty bread.