Wash mussels well and remove beards
Bring water to a boil, add mussels, cover and cook until all shells are open.
Remove mussels and chill, strain the stock through a China cap and reserve.
Remove mussels from the shells, chop and set aside until needed..
Saute onions and celery in olive oil until softened. Dust with flour to make roux.
Add hot stock, stir to dissolve roux, bring to a boil then simmer.
Add potatoes and thyme, let simmer for 30 minutes, until potatoes are tender.
Add chopped mussels to the soup, continue to simmer
Add half and half, parsley and seasoning.
Taste and adjust seasoning if necessary, serve.