Remove salmon from refrigerator 15–20 minutes before cooking to take off chill. Pat fillets dry with paper towels. Sprinkle both sides with kosher salt (use slightly less on the underside if fillets are skin-on) and evenly grind the black pepper over the top. Rub lemon zest and minced garlic lightly over the flesh side.

Score skin (if thick)

If the skin is very thick, make 2 shallow diagonal cuts through the skin (not deep into flesh) so the fillet will lay flat and not curl while cooking.

Cook salmon

Heat pan

Place a large nonstick or stainless-steel skillet over medium-high heat. Add 1 tablespoon of olive oil and let it heat until shimmering but not smoking (about 1 minute).

Sear skin-side down

Place the salmon fillets skin-side down in the pan, spacing them so they don't touch. Press gently with a spatula for 10 seconds to ensure full contact. Reduce heat to medium and cook skin-side down, undisturbed, for 4–5 minutes for 1-inch-thick fillets (longer for thicker fillets) until the skin is crisp and the flesh is cooked about two-thirds of the way up the side.

Flip and finish

Add 1 tablespoon olive oil and 1 tablespoon butter to the pan around the fillets. Flip fillets carefully to flesh-side down and cook 1–2 minutes to finish (or 3–4 minutes for thicker pieces) until an instant-read thermometer reads 50–55°C (122–131°F) for medium-rare to medium, or 60°C (140°F) for well done. Spoon pan juices over the top once or twice while finishing.

Make pan sauce

Remove salmon and reserve

Transfer cooked fillets to a warm plate and loosely tent with foil to rest while you make the sauce. Keep the skillet over medium heat; there should be browned bits in the pan.

Sauté shallot

Add the remaining 1 tablespoon butter to the skillet. Add the chopped shallot and sauté for 1–2 minutes until softened and translucent, stirring to deglaze the pan.

Deglaze

Pour in the white wine (or broth) and scrape up browned bits with a wooden spoon. Let the liquid reduce by about half, 1–2 minutes.

Finish sauce

Stir in lemon juice, whole grain mustard, and honey/maple syrup. Reduce heat to low and whisk in the cold butter (if any remains) or swirl the pan to emulsify for 30 seconds until glossy. Stir in chopped dill. Taste and adjust seasoning with a pinch of salt and pepper if needed.

Coat fillets

Return the salmon to the pan briefly (30 seconds) spooning the sauce over the fillets to warm and coat them.

Serve

Plate each fillet, spoon additional sauce over the top, garnish with lemon wedges and microgreens or parsley. Serve immediately with your choice of sides (rice, roasted vegetables or salad).