Brush the mussels thoroughly under cold running water.
Remove the beards.
Place in a bowl with cold water and remove any open mussels.
Peel and finely chop the onion and garlic. Saute in a pan with hot oil until softened.
Wash and chop the leeks. Peel and finely dice the carrot. Add both to the pan and cook briefly.
Sprinkle with the parsley.
Pour in the wine and simmer for 5 minutes.
Drain the mussels in a sieve.
Add to the vegetables in the pan, cover and cook, shaking occasionally, for about 5 minutes until the mussels open.
Remove the mussels from the pan, discard any unopened ones and serve with a little of the cooking liquid.
Eat using one shell to detach the flesh from the other side.