Season both sides of each fillet evenly with the salt, black pepper, smoked paprika, and lemon zest. Let rest at room temperature for 10 minutes while you prepare the pan and sauce ingredients.

Pan sauce / finishing

Cook halibut

Heat a large heavy skillet (preferably stainless steel or cast iron) over medium-high heat. Add the olive oil and 1 tablespoon of the butter. When the fat is hot and shimmering but not smoking, add the halibut fillets spaced apart. Cook undisturbed for 3–4 minutes until the underside is golden-brown and releases easily from the pan. Flip gently with a spatula and cook the second side 2–3 minutes more, or until the fish registers 125–130°F (52–54°C) for medium, or 140°F (60°C) for well done. Transfer fillets to a warm plate and tent loosely with foil to rest.

Make pan sauce

Lower the heat to medium. Add the remaining 2 tablespoons butter to the same skillet. Add the minced garlic and minced shallot and sauté 30–45 seconds until fragrant and translucent but not browned. Pour in the white wine (or chicken broth) to deglaze the pan, scraping up browned bits with a wooden spoon. Let the liquid reduce by about half, 1–2 minutes.

Stir in the fresh lemon juice and capers, then swirl in the butter to emulsify the sauce. Taste and adjust seasoning with a pinch of salt and pepper if needed. Remove from heat and stir in the chopped parsley.

Spoon the sauce over the rested halibut fillets. Garnish with lemon wedges and microgreens or extra parsley, if using. Serve immediately.