Pat the cod fillets dry with paper towels. Season both sides evenly with kosher salt (about 1/2 tsp per fillet) and freshly ground black pepper. Lightly dredge each fillet in the flour, shaking off excess. Place on a plate and let rest for 5–10 minutes while you preheat the pan.

Cook the cod

Heat a large heavy skillet (cast-iron or stainless steel) over medium-high heat until hot. Add 2 tablespoons olive oil and 1 tablespoon butter. When the butter stops foaming and the oil shimmers, add the cod fillets presentation-side down (skin-side down if skin-on). Cook undisturbed for 3–4 minutes until the underside is golden and releases easily. Flip carefully with a spatula and cook the other side 2–4 minutes, depending on thickness, until the fish is opaque and flakes easily (internal temp ~63°C/145°F). Transfer fillets to a warm plate and tent loosely with foil.

Make the lemon-butter sauce

Reduce heat to medium. In the same pan, add the remaining 2 tablespoons butter. Add the minced shallot and sauté 1–2 minutes until softened and translucent. Add the minced garlic and cook 30 seconds until fragrant (do not brown). Pour in 60 ml white wine (or stock) to deglaze the pan, scraping up browned bits; simmer 1–2 minutes to reduce slightly. Stir in 2 tablespoons fresh lemon juice, 1 teaspoon lemon zest, and the rinsed capers if using. Reduce heat to low and swirl in the remaining butter to emulsify the sauce into a glossy consistency. Taste and adjust seasoning with a pinch of salt and pepper.

Finish and serve

Return the cooked cod to the pan briefly (30 seconds) to warm through and coat with sauce, or spoon sauce over fillets on the serving plate. Sprinkle 2 tablespoons chopped parsley and 1 tablespoon chopped chives or dill over the fish. Add a final grind of black pepper. Serve immediately with lemon wedges.

Accompaniments (optional)

Boiled or roasted potatoes: If using potatoes, quarter small potatoes and simmer in salted water until tender (12–15 minutes) or toss with 1 tbsp olive oil, salt, and roast at 200°C/400°F for 25–30 minutes until golden. Steam or blanch green vegetables until bright and tender-crisp (3–5 minutes), then toss with a pinch of salt and a little butter or olive oil.