Sole (or in this case Flounder) in the style of the Miller's Wife
The recipe is a French classic, and makes for a very nice piece of fish. The technique is from Escoffier, and isn't just restricted to flatfish; it also has the advantage of being a good recipe to know as it cooks very quickly. The technique is slightly modified from Escoffier's; the butter in the pan sauce isn't browned.
3 filets of flounder or sole (about 1 lb/500g)
3 tbsp unsalted butter
2 tbsp chiffonaded parsley
juice of one lemon
flour
kosher salt
pepper
Rinse and pat dry the fish filets; sprinkle with kosher salt and pepper and dredge lightly in flour. In a saute pan on medium-high heat, melt half the butter. When it's hot, add the fish filets and saute over medium-high heat until just cooked through (keep a close eye on it; it will cook in a matter of 3-5 minutes at most). Remove filets to a platter or individual serving dishes; melt remaining butter in pan and add lemon juice and parsley, stirring to deglaze. Pour sauce over fish filets and serve.
Since this is a French recipe, a white wine is mandatory.