Sole Meuniere (Sole in Lemon-Butter Sauce)

Method

1. Preheat the oven to 250 degrees F (120 degrees C). Place 2 serving plates in the oven to pre-warm.
2. Divide oil between 2 large skillets and heat over medium heat until oil shimmers.
3. While oil is heating, sprinkle salt and pepper over both sides of fillets. Pour flour into a pie plate and dredge fillets on both sides until evenly coated.
4. Add butter evenly to both skillets and swirl to mix with oil. When foam subsides, add fish and cook until golden brown, 2 to 3 minutes per side.
5. Carefully turn fish over and cook until opaque white in the middle and starting to brown on the bottom, 1 to 2 minutes more. Transfer fish to the warmed plate and loosely cover with aluminum foil. Return plates to the oven.
6. Return skillets to medium-high heat. Add butter and cook until golden brown, 1 to 2 minutes. Remove from heat and stir in parsley and lemon juice. Spoon butter sauce over fish.