Set the oven to 425℉. While it heats, let the salmon sit at room temperature.
When the oven temp has reached 425℉, place a cast iron skillet (or other skillet with an oven safe handle) over medium high heat for 2-4 minutes, until small drops of water sprinkled on its surface sizzle and immediately evaporate. Blot the salmon firmly with a paper towel; the drier the surface, the better the sear. Sprinkle generously with salt and pepper.
Add the oil to the pan and swirl to coat. It should shimmer and spread easily in the very hot skillet. Without delay, gently lay the salmon in the oil, skin side up. Leave an inch of space between filets; an overcrowded pan would cause them to steam instead of searing.
Cook the salmon, undisturbed, for 2 to 3 minutes. A golden brown crust will develop on the bottom surface of the fish, visible at the edges where the salmon touches the pan. Resist the urge to peek underneath: trust the crust! It will continue to form in the oven. The less you disturb the salmon during cooking, the better.
Transfer the entire skillet, with the salmon still skin side up, to the hot oven to roast for 6 to 10 minutes, depending on the thickness of the filets and your desired doneness. For fully cooked filets that are flaking but still moist, a 1-inch thick fillet usually takes 7 to 8 minutes in the oven and will measure 120-125℉ in the center. Remove the pan from the oven, noting that it will be scalding hot and the oil sizzling!
Using a thin spatula, carefully remove the filets from the pan to prevent overcooking. Serve, crust side up, with a squeeze of lemon or the sauce or garnishes of your choice.