Remove the salmon from the refrigerator 15 minutes before cooking to let it come to room temperature.
Heat a 10–12 inch frying pan over medium-high until very hot. Test by flicking a few drops of water into the pan — they should dance and evaporate quickly.
Add 1–2 tablespoons of neutral, high-smoke-point oil and swirl to coat the bottom; heat until shimmering but not smoking.
Pat the fillets dry on all sides with paper towels. Season the flesh side with kosher salt and a few grinds of black pepper.
Carefully add the fillets to the pan skin-side down, placing them from front to back to avoid splatter toward you. Reduce heat to medium or medium-low.
When the fillets first hit the pan they may buckle; gently press the flesh with a fish spatula for about 1 minute until the fillets lay flat again.
Cook skin-side down until the fish is about 3/4 cooked through, watching for the color change from translucent coral to opaque pastel up the sides — about 5–9 minutes depending on thickness and stove.
Flip the fillets with a fish spatula and cook the flesh side 1–4 minutes more to your desired doneness (120–125°F for medium-rare, 125–130°F medium, 145°F well done per USDA).
Remove the fillets from the pan and drain briefly on a paper towel–lined plate for 2–3 minutes. Serve skin-side up for crispy skin or loosen and remove the skin if desired.
Optionally finish with a squeeze of fresh lemon juice or your preferred sauce before serving.