Season fish fillets with salt and pepper, then dredge lightly in flour.
Heat olive oil and 1 tbsp butter in a large skillet over medium-high heat. Cook fillets mostly on one side (~3–4 min) until golden, then flip and cook 1–2 min more. Remove to a plate.
In the same pan, add wine and lemon juice, scraping up browned bits. Let reduce slightly.
Swirl in remaining 2 tbsp butter and the capers. Stir until the sauce emulsifies.
Spoon sauce over fish, garnish with parsley, and serve with a side of angel hair pasta or roasted vegetables.
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