Pat the salmon fillets dry and sprinkle both sides with a pinch of salt and pepper. Set aside.
Preheat a heavy pan, such as cast iron, over high heat. You will know it’s ready when a few drops of water quickly start to bubble rapidly, as if they are boiling on the surface of the pan.
Wait until any water has disappeared, then add the oil to the pan. Use enough to cover the bottom of the pan with a thin layer of oil.
When the oil has heated up (it should be shimmering slightly), place the salmon fillets in the pan with at least an inch of space surrounding each.
Cook until you can see a crust forming on the bottom. Don’t pick them up. You should be able to see it by looking at the side of the fillet in the pan. By the way, don’t stick your face in the pan to try to view the crust – the oil might spatter and burn you. If you can’t see the crust yet, it’s not full formed. Mine took 3.5 minutes, but yours could take anywhere from 2-5 minutes, depending on the flame, your pan and the size and shape of your fillets.
Once the crust has formed, cover the pan with a top or piece of foil, leaving it cocked so that there is a sliver of room for steam to escape. Cook for 2-4 more minutes until the tops of the fillets look almost opaque, but the center area is still pink.
Serve immediately if you like a medium filled, but let the fillets sit for a couple of minutes in the pan with the flame off, or on a plate (the residual heat will continue to cook them), if you like your salmon closer to well done.