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1
In a small bowl, soak the capers in cold water for 45 minutes.
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2
Drain and pat dry.
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3
Season the fish with salt and pepper.
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4
In a shallow bowl, whisk the flour with 1 teaspoon each of salt and pepper.
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5
Dredge the fillets in flour and shake off any excess; transfer to a platter.
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6
In a large skillet, melt 2 tablespoons of the clarified butter over moderately high heat.
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7
Add 4 sole fillets to the skillet and cook, turning once, until golden brown on both sides, about 4 minutes total.
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8
Transfer to a platter.
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9
Repeat with the remaining clarified butter and sole fillets.
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10
Add the capers to the skillet and cook over moderately high heat until lightly browned and fragrant, about 30 seconds.
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11
Add the white wine and lemon juice and cook over moderately high heat until reduced to 2 tablespoons, about 1 minute.
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12
Remove the skillet from the heat and add the butter, a few pieces at a time, whisking until the butter is melted before adding more.
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13
Add half of the parsley and season the sauce with salt and pepper.
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14
Pour the warm sauce over the sole and garnish with the remaining parsley.
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15
Serve immediately.