Prep the oven and pan: Heat the oven to 400°F (200°C). If you plan to finish under the broiler, set the rack 6 inches from the element. Pat salmon dry with paper towels.
This helps the surface brown.
Season the salmon: Sprinkle both sides with salt. Dust the top with lemon pepper and a bit of black pepper if needed. If the fillets are very thick, season the sides too.
Make the garlic butter: In an oven-safe skillet over medium heat, melt the butter with olive oil.
Add minced garlic and cook 30–45 seconds, just until fragrant. Stir in lemon zest and 1 tablespoon lemon juice. Remove from heat to prevent burning.
Sear the salmon: Return the skillet to medium-high.
Nestle salmon fillets skin-side down. Cook 2–3 minutes until the skin crisps and the edges look opaque about 1/4 inch up.
Baste: Spoon the hot garlic butter over the tops of the fillets several times. This builds flavor and keeps the salmon moist.
Finish in the oven: Transfer the skillet to the oven.
Roast 5–8 minutes, depending on thickness, until the salmon flakes easily with a fork and reaches 125–130°F for medium or 135°F for medium-well. If you want extra color, broil for the last 1–2 minutes. Don’t walk away.
Rest and sauce: Take the skillet out and let the salmon rest 2 minutes.
Squeeze over more lemon juice to taste and swirl the pan to combine with the butter. Taste the sauce and adjust salt and lemon.
Garnish and serve: Top with chopped parsley or dill. Spoon the pan sauce over each fillet.
Serve with rice, roasted potatoes, or a crisp salad.