Pat the fillets dry with paper towels. Season both sides evenly with the kosher salt and black pepper. Lightly dust each fillet with the flour, shaking off excess so there is just a thin coating.

Heat the pan

Place a large nonstick or stainless-steel skillet over medium-high heat. Add the olive oil and 1 tablespoon of the butter. Heat until the oil shimmers and the butter foams but does not brown.

Sear the fish

Place the fillets in the hot pan presentation side down (skin side down if skin-on). Do not crowd the pan; work in batches if needed. Cook without moving 3–4 minutes until the underside is golden and releases easily. Flip and cook the other side 2–4 minutes more, until the internal temperature reaches 130–135°F (54–57°C) for moist, flakey fish or cooked through as desired. Transfer fillets to a warm plate and tent loosely with foil.

Make the pan sauce

Reduce heat to medium. Add the remaining 1 tablespoon butter to the skillet. Add the minced shallot and cook 1–2 minutes until softened and translucent, stirring to scrape the fond (browned bits) from the pan. Add the garlic and cook 30 seconds until fragrant.

Deglaze and finish sauce

Pour in the white wine (or stock) to deglaze the pan, scraping any browned bits. Let the liquid simmer and reduce by about half (about 2–3 minutes). Stir in the lemon juice, capers, and chopped parsley. If desired, whisk in the optional extra tablespoon of butter to create a glossy finish. Taste and adjust seasoning with a pinch of salt and pepper if needed.

Serve

Return the fillets to the pan briefly (30 seconds) to warm through and coat with sauce, or spoon the sauce over the plated fillets. Garnish with lemon wedges and extra parsley or microgreens. Serve immediately.

Optional garnish & sides

Serve fish with lemon wedges for squeezing. Pair with simple sides such as steamed vegetables, roasted potatoes, or a light salad. Sprinkle microgreens or extra parsley on top for color and freshness.