Pat the salmon dry. Use paper towels to remove excess moisture. This helps the skin crisp and prevents sticking. Season both sides with salt, pepper, and paprika if using.

Preheat the pan. Set a large stainless steel or cast-iron skillet over medium-high heat. Add the olive oil and let it heat until shimmering.

Sear the salmon, skin side down first. Place the fillets in the pan and press gently with a spatula for 10 seconds to prevent curl. Cook without moving them for 4–5 minutes, until the skin is crisp and the fish is mostly opaque up the sides.

Flip and finish. Turn the fillets and cook 1–2 minutes more, depending on thickness. Aim for medium doneness, about 125–130°F in the thickest part. Transfer to a plate and tent loosely with foil.

Make the brown butter. Reduce the heat to medium. Add the butter to the same pan. Let it melt and bubble, stirring or swirling as it foams. After 2–3 minutes, the milk solids will turn golden and smell nutty.

Add aromatics and lemon. Stir in the garlic and cook 20–30 seconds, just until fragrant. Remove the pan from heat and add lemon zest, lemon juice, and capers. Taste and season with a pinch of salt and pepper.

Return the salmon. Spoon some sauce into the pan and nestle the fillets back in, skin side up, to warm through for 30–60 seconds. Baste with the brown butter sauce.

Finish with herbs. Sprinkle with parsley or chives. Serve right away with extra lemon wedges and any remaining sauce poured over the top.