Pat the salmon dry. Use paper towels to remove moisture so the fish sears well.
Season both sides with salt, pepper, and a light sprinkle of smoked paprika if you like.
Preheat your pan. Set a large skillet over medium to medium-high heat. Add olive oil and 1 tablespoon butter. When the butter foams, the pan is ready.
Sear the salmon skin-side down. Place fillets skin-side down and press gently for 10 seconds so the skin doesn’t curl.
Cook 4–5 minutes until the skin is crisp and the color turns opaque halfway up the sides.
Flip and finish. Turn the salmon and cook another 2–3 minutes, depending on thickness. Remove to a plate and tent loosely with foil.
Make the lemon butter sauce. Lower heat to medium-low. Add remaining 3 tablespoons butter to the pan.
Stir in minced garlic and cook 30–45 seconds until fragrant, not browned.
Add lemon and herbs. Stir in lemon zest and juice. If the sauce seems too thick or sharp, add a splash of broth. Simmer 30 seconds, then remove from heat.
Stir in chopped parsley or dill.
Return the salmon. Place fillets back in the pan to coat with sauce, spooning it over the tops. Taste and adjust salt, pepper, or lemon to preference.
Serve. Plate salmon with more sauce, garnish with extra herbs and lemon slices. Great with roasted asparagus, sautéed zucchini, or a simple arugula salad.