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Step 1
Remove the salmon from the refrigerator and let stand at room temperature for at least 10 minutes. With a paper towel, pat the fillets very dry on both sides.
Step 2
Heat the butter and oil in a 12-inch cast iron or heavy stainless steel skillet over medium-high heat until the butter foams and the foam subsides, about 3 minutes. It’s important the pan is VERY hot before you add the salmon, or it won’t crisp properly.
Step 3
Just before adding it to the pan, season the flesh side of the salmon with 1/2 teaspoon salt and pepper.
Step 4
Carefully place the fillets in the skillet, skin-side up, lowering them down away from you to protect yourself from splatters. Sprinkle the skin side of the salmon with a pinch of kosher salt.
Step 5
Let the salmon cook on the first side completely undisturbed until the flesh appears cooked about 3/4 of the way up the fillet, about 5 to 6 minutes.
Step 6
With a fish spatula or similar long, wide, flexible spatula, carefully flip the fillets. They should release easily from the pan; if they are sticking, the salmon most likely isn’t ready yet. Let cook another 30 seconds or so, then try again.
Step 7
Reduce the pan heat to medium. Cook the salmon on the other side for 2 to 4 minutes more, until it is done to your liking (I remove the salmon at 130 degrees for medium). Remove to a plate and let rest 5 minutes. Squeeze lemon over the top and sprinkle with herbs. Serve hot or at room temperature.