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1
Preheat 2 medium non-stick skillets over medium-low heat for 5 minutes.
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2
Meanwhile, lay the fillets on a piece of wax paper, parchment, or a baking sheet and blot dry with paper towels.
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3
Season the fillets with salt and pepper.
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4
(If the fillets tapers down to a very thin tail, fold the tail back to make a more uniformly thick fillet.)
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5
Put the flour on a plate.
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6
Dredge the rounded-sides of the fillets in the flour and shake off any excess.
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7
Raise the heat to medium-high and add 1 tablespoon of butter to each skillet.
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8
When the butter stops foaming, add 2 fillets to each pan, rounded-side down, and cook, lightly shaking the skillets occasionally, until golden brown, about 2 minutes.
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9
Turn off the heat, flip the fillets with a spatula, and let the fillets finish cooking in the residual heat in the pans, about 2 minutes more.
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10
Transfer the fillets to 4 warm plates and cover loosely with foil.
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11
Add the lemon juice and water to one of the skillets.
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12
While moving the skillet in a circular motion, add the remaining 3 tablespoons butter, little by little, until melted and a smooth, creamy sauce is formed.
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13
Stir in the parsley and thyme and season with salt and pepper to taste.
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14
Spoon some of the sauce over each fillet and serve immediately.
