Pour the mixture of 2/3 dry white wine and 1/3 white or spirit vinegar into a frying pan.
Add the chopped shallots
Bring to the boil over a medium flame and reduce by ¾, keeping some of the liquid.
Cook the flour thoroughly in the butter to avoid an uncooked floury taste.
Add your butter piece by piece (cold from the refrigerator and cut into cubes), stirring well with a whisk and keeping gently on the boil.
If you want an even more luxuriously tasty dish, use 100% cream.
Let the mixture boil, stirring all the time.
Add the fish filets and simmer gently (for 5 to 15 minutes depending on the kind of fish).
Score the back of each fillet in several places so that it remains flat after cooking.
Serve on a family-size dish.