This one is much simpler than you might think, and is always very impressive to serve. For two people, you will need about a pound weight (500-600 grams) of Mussels - this seems to be the usual size available at the fish counters in supermarkets.
The secret of success is carefully cleaning and selecting the Mussels. Under running water from the cold tap, scrape each mussel clean, including the dangling green "beards". You must discard any mussel which is open and does not close when tapped sharply - it will be off and definitely not good for you! Put the cleaned mussels in a large bowl of fresh water and rinse well.
You will need a large pan with a tight-fitting lid. An ordinary saucepan will do, but there are special pans available with a particularly deep lid, which can be used to serve at the table - the lid doubles as a repository for the empty shells.
Melt a teaspoon of butter with a tablespoon of olive oil in the pan. Peel and finely slice three shallots, or perhaps half a medium onion. Cook the shallots gently in the oil and butter for perhaps 5 minutes until soft.
To the shallots add half a bottle of dry white wine - I use the cheapest stuff I can find for this, or at least some left-overs from a party.
Also add half a teaspoon of dried parsley, and half a teaspoon of dried thyme, and a dried bayleaf. If you can get fresh herbs, so much the better: wash and chop very finely before adding. Add some freshly-ground black pepper and simmer for about 10 minutes.
Add the mussels to the wine in the pan and cover, cooking for about 5 minutes and shaking often. (This is why you need a well-fitting lid for the pan!)
Scoop out the mussels and place in two warmed dishes. Remove any which have not opened during cooking. Bring the remaining wine to the boil, thick slightly by adding a teaspoon of cornflour (dissolved in a little cold water), and then pour the resulting sauce over the mussels.
Serve with lots of warm crusty bread and a fine chilled Chablis, or perhaps in the Belgian style with chips (french fries, pomme frites) and blond (light-coloured) beer.