Preheat the oven to 400 degrees . In a small bowl, whisk together the brown sugar, mustard, lemon juice and 1/2 teaspoon pepper.
Heat a large, ovenproof skillet over high heat. Rub the salmon with the oil, season with salt and pepper and place skin side up in the skillet. Cook until a crisp brown crust forms, about 3 minutes. Remove from the heat, flip the salmon and coat with the brown sugar mixture. Transfer the skillet to the oven and bake until the glaze caramelizes and the fish is cooked through, about 5 minutes.