Melt the butter with the olive oil in a large heavy-bottomed pan over medium heat. Add in the leeks and celery, and cook, stirring occasionally, for 6 to 7 minutes or until the vegetables are soft. Add the garlic and continue cooking, while stirring, for 1 minute more.
Drop in the mussels and stir the ingredients together gently until combined. Add the wine and thyme sprigs, cover the pan and simmer for 6 to 7 minutes. Stir in the cream, cover and simmer for another 5 minutes or until the mussels open.
Serve with lots of crusty bread to soak up the sauce.
Discard any mussels that haven't opened in that time.
Recipe courtesy of William Granger