Season the fish with salt and pepper generously on both sides. Dip in the flour so that both sides of the fillets are covered.
Heat the oil in an oven safe, skillet over high heat. When it's hot, add the fillets to the pan with plenty of space between the pieces of fish. Cook until browned on both sides, about 3 minutes per side.
Put the pan in the oven and roast until the fish is barely translucent in the center, 10 minutes, depending on the thickness of the fillets. Watch them carefully and take them out before they begin to flake. Enjoy Oven Roasted Halibut!