Pat the salmon dry. Season both sides with salt and pepper. Dry fish sears better and helps the glaze stick.
Whisk the glaze. In a bowl, combine coconut milk, lime zest, lime juice, honey or brown sugar, soy sauce, garlic, ginger, and red pepper flakes if using. Taste and adjust.
It should be bright, a little sweet, and slightly salty.
Heat the pan. Set a large skillet over medium-high heat. Add oil and heat until it shimmers.
Sear the salmon. Place fillets in the pan, skin-side down if using skin-on. Cook 3–4 minutes until the skin is crisp and the edges turn opaque.
Flip and cook another 1–2 minutes. Remove salmon to a plate; it will finish in the glaze.
Reduce the glaze. Lower heat to medium. Pour the coconut-lime mixture into the pan.
Stir and let it bubble gently, about 3–5 minutes, until slightly thickened and glossy. You want it to coat the back of a spoon.
Finish the fish. Return salmon to the pan, spooning glaze over the top. Cook 2–4 minutes, depending on thickness, until the salmon flakes and is just cooked through.
Aim for medium for the most tender texture.
Garnish and serve. Sprinkle with chopped cilantro or sliced scallions. Serve over rice or vegetables with extra glaze spooned on top.
Optional oven method. Prefer hands-off? Place seasoned salmon on a lined sheet pan.
Bake at 400°F (200°C) for 8–10 minutes, depending on thickness. Meanwhile, reduce the glaze on the stove, then spoon it over the baked salmon to finish.