The word meunière is a reference to the miller of wheat, whose wife (according to French lore) cooked everything coated with flour. The original French style of trout meunière was coated with seasoned flour, sautéed in butter, and then topped with the browned butter from the pan. This is still more or less how the dish is done in some restaurants—notably Galatoire’s.
But there’s a Creole version and I like it better than the French classic. It was invented by Count Arnaud, wh