Pour the milk into a baking dish for dipping the fish; mix the flour with salt and pepper on a plate; melt the clarified butter in a frying pan until sizzling hot and foaming.
Dip the sole first in the milk, then in the seasoned flour to coat, shaking off any excess.
Fry immediately until done, 3 to 5 minutes per side, depending on the size.
Remove to a warm serving dish.
Pour the brown butter into the pan.
As soon as it’s hot, add the garnish of parsley, and immediately pour it over the fish.
Squeeze over lemon juice, and serve right away.
*Brown butter is achieved by simply leaving melted butter on the heat long enough to turn a golden colour. Don't let it burn, obviously.
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