Heat the oil a medium frying pan over high heat until shimmering (there should be a thin coating of oil over the entire surface of the pan—add more if needed). Meanwhile, pat the salmon dry with paper towels and generously season both sides with salt and pepper.
Lay the salmon skin-side down in the pan and reduce the heat to medium low. Do not move the fish. Cook, undisturbed, until the skin is deeply browned and crispy and the salmon is cooked about three-quarters of the way through, about 7 minutes (the salmon should easily release from the pan; if it doesn’t, let it cook a minute more).
Using a flat metal spatula or fish spatula, flip the salmon and cook until it’s just barely opaque in the center, about 3 minutes more. Serve immediately, skin-side up.