How to Make It
In a small bowl, soak the capers in cold water for 45 minutes. Drain and pat dry.
Season the fish with salt and pepper. In a shallow bowl, whisk the flour with 1 teaspoon each of salt and pepper. Dredge the fillets in flour and shake off any excess; transfer to a platter.
In a large skillet, melt 2 tablespoons of the clarified butter over moderately high heat. Add 4 sole fillets to the skillet and cook, turning once, until golden brown on both sides, about 4 minutes total. Transfer to a platter. Repeat with the remaining clarified butter and sole fillets.
Add the capers to the skillet and cook over moderately high heat until lightly browned and fragrant, about 30 seconds. Add the white wine and lemon juice and cook over moderately high heat until reduced to 2 tablespoons, about 1 minute. 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. Add half of the parsley and season the sauce with salt and pepper. Pour the warm sauce over the sole and garnish with the remaining parsley. Serve immediately.