Season the salmon with the salt and a few grinds of pepper. Heat the oil in a 12-inch nonstick skillet over medium-high heat until hot and shimmering. Cook the salmon, without moving, skin side up, until golden and crisp, about 4 minutes. Carefully flip the fillets and reduce the heat to medium. Continue cooking until done to your liking, 4 to 5 minutes more. Transfer to a platter and serve.