Ask your fishmonger to just take the flounder heads off and to trim their fins (this isn’t so tricky to do at home with hefty scissors or a sharp knife)
Put some plain flour and some salt and pepper on a plate, and gently flour your fish before putting them in a hot pan with some Extra Virgin Olive Oil
Fry them for a few minutes (3 – 5) before turning them – and don’t shake the pan around; you are looking to get a good crust on each side
Give them the same on the other side before serving quickly with a big slice of lemon.
Chippy-style chips are clearly off the menu, but roasted potatoes (in olive oil) do the job here perfectly, and if you are living dangerously you could have a little spoonful of mayonnaise (0% greek yoghurt suffices perfectly well!). Some kind of salsa verde is also really good with this fish.