Step 1

Preheat the oven to 250 degrees F (120 degrees C). Place 2 serving plates in the oven to pre-warm.

Step 2

Divide oil between 2 large skillets and heat over medium heat until oil shimmers.

Step 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.

Step 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.

Step 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.

Step 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.