Preheat the oven to 475 degrees F.
Set a 10-inch heat-proof saute pan over medium heat for 2 minutes. Brush the fillet with the oil and sprinkle with kosher salt and black pepper. Place the fillet in the pan flesh side down and cook for 3 minutes. Turn the fillet over, place pan in the oven, and cook for 5 minutes. Transfer the fillet to a plate, cover loosely with foil, and let rest for 5 minutes before serving.