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Step 1
Press salmon fillets between paper towels to dry surfaces thoroughly. Season on all sides with salt and pepper.
Step 2
In a large stainless, cast iron, or carbon steel skillet, heat oil over medium-high heat until shimmering. Reduce heat to medium-low, then add a salmon fillet, skin side down. Press firmly in place for 10 seconds, using the back of a flexible fish spatula, to prevent the skin from buckling. Add remaining fillets one at a time, pressing each with spatula for 10 seconds, until all fillets are in the pan.
Step 3
Cook, pressing gently on back of fillets occasionally to ensure good contact with skin, until skin releases easily from pan, about 4 minutes. If skin shows resistance when you attempt to lift a corner with spatula, allow it to continue to cook until it lifts easily. Continue to cook until salmon registers 110°F (43°C) in the very center for rare, 120°F (49°C) for medium-rare, or 130°F (54°C) for medium, 5 to 7 minutes total.
Step 4
Using spatula and a fork, flip salmon fillets and cook on second side for 15 seconds, then transfer to a paper towel–lined plate to drain. Serve immediately.