Step 1: Pat fish dry with paper towels and season each fillet with salt and pepper.
Step 2: Place flour in a pie plate (or equivalent size plate). Dredge the fish in the flour, shaking off any excess. Transfer each fish fillet to a clean plate.
Step 3: In a large size skillet, heat 2 tbsp. extra virgin olive oil. When the oil is heated through and hot, melt in 1 tbsp. butter. When butter is melted and foamy, carefully add 2 fillets and cook for approximately 2 to 4 minutes per side, until the fish is opaque in the center.
Step 4: Transfer the fish to a warm clean tray.
Step 5: Add 2 more tablespoons of olive oil and 1 tablespoon butter to the skillet. Repeat cooking the remaining fillets as done prior. Transfer fillets to the warm tray.
Step 6: Pour off grease (if necessary), leaving about 1 ½ - 2 tablespoons in the skillet. Add 1 tbsp. butter.
Step 7: When the butter melts, add the lemon slices and cook, turning once, until lightly browned, 2 to 3 minutes. Place the lemon slices evenly on top of the fish fillets.
Step 8: To the skillet, add the shallots and garlic. With wooden spoon, scrape up the brown bits to release flavors and cook garlic and shallots until softened for about 1 minute (being careful not to burn the garlic or else it will become bitter and will change the nature and flavor of the sauce).
Step 9: Add the wine, capers, lemon juice, and parsley. Simmer for approximately 1 minute. Check for seasoning and adjust with salt and pepper. Also check for acidity and correct with a pinch or two of sugar, if necessary.
Step 10: Remove the skillet from the stove top and gently swirl in the remaining 1 - 2 tbsp. butter until the sauce thickens slightly and is shiny/glazey looking.
Step 11: Return the fillets to the sauce to warm for 5 - 6 minutes. Transfer fillets to warm plates and pour sauce over each. Serve and enjoy. Pairs very well with rice.
Step 12: NOTE: I normally like extra sauce so I double it!
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