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. Cook's Note: Discard any mussels that haven't opened in that time.
Serve with lots of crusty bread to soak up the sauce.