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How to clarify butter: Melt the butter slowly.
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Let it sit for a bit to separate.
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Skim off the foam that rises to the top, and gently pour the butter off of the milk solids, which have settled to the bottom.
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A stick (8 tablespoons) of butter will produce about 6 tablespoons of clarified butter.
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Arrange the fillets in a shallow dish and pour the milk over them.
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Let soak for at least 5 minute and up to 20 minute Set up your work area so that you can move quickly: position your serving plates or platter, the milk soaking pan, a pile of paper towels, and the seasoned flour on a plate.
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Have the melted butter in a small, heavy-based saucepan, and the lemon juice and parsley ready for action.
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In one or two large frying pans, heat the clarified butter over medium-high heat until very hot but not quite smoking.
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Lift a fillet from the milk, blot it on the paper towels, dip it into the flour, and shake off the excess.
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Carefully lay the fish in the hot fat.
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Repeat with the other fillets, but don't overcrowd the pan or you'll have trouble flipping.
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Adjust the temperature to keep the fat sizzling briskly but not burning.
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Cook the fish until golden on one side, about 2 minute With a slotted spatula, a large spoon, and great care, gently flip the fish.
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When the second side of the fish is golden brown and the flesh is tender when poked with a sharp knife in the thickest part, use the slotted spatula to remove the sole, set it on paper towels to drain briefly, and arrange on the warm platter or plates.
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When all the fillets are cooked, heat the melted whole butter carefully over medium-high heat, swirling the pan occasionally, until the butter is fragrant and the milk solids turn nutty brown; remove the pan from the heat so the butter doesn't keep cooking, but keep it hot.
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Working fast, pour 1 Tbs.
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of the lemon juice evenly over each fish and sprinkle on the parsley.
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Pour about 1-1/2 Tbs.
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of the hot browned butter on each fish -- if all has gone well, you'll see and hear a delicious sizzle.
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(If there's no sizzle, it will still taste great.)
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Serve immediately.
