Prep the salmon: Pat the fillets dry with paper towels.
Season both sides lightly with kosher salt and black pepper. Dry fish browns better and helps the glaze stick.
Heat the pan: Preheat your oven to 400°F (200°C). Set a large oven-safe skillet (cast iron or stainless) over medium-high heat.
Add olive oil and let it shimmer.
Sear skin-side down: Place salmon in the pan skin-side down. Press gently with a spatula for 10 seconds so the skin makes good contact. Sear for 3–4 minutes until the skin is crisp and the sides turn opaque about one-third up.
Flip briefly: Carefully flip and sear the flesh side for 30–45 seconds.
You’re just getting a little color; it will finish in the oven.
Make the glaze: Remove salmon to a plate (skin-side up). Lower heat to medium. In the same pan, add butter and garlic.
Cook 30–45 seconds until fragrant, not browned. Stir in brown sugar, soy sauce, lemon juice, and a pinch of red pepper flakes if using. Simmer 1–2 minutes until glossy and slightly thickened.
Coat and bake: Return salmon to the skillet, skin-side down.
Spoon glaze over the tops and sides. Transfer the skillet to the oven and bake 5–7 minutes, depending on thickness, until the salmon flakes easily with a fork and reaches 125–130°F for medium.
Finish under the broiler (optional): For extra caramelization, broil 1–2 minutes. Watch closely to avoid burning the sugar.
Rest and serve: Let the salmon rest 2 minutes.
Spoon any remaining glaze from the pan over the fillets. Garnish with chopped parsley or chives and serve with lemon wedges.