Remove the tenderloin from the freezer. Using an electric knife, cut the beef into 3/8-inch thick slices. Place slices of beef, 1 at a time, between 2 pieces of plastic wrap. Squirt the beef lightly with water and squirt the top of the plastic wrap as well. Pound to no less than 1/8-inch thickness. Lightly brush each slice of beef on both sides with vegetable oil and season with salt and pepper on both sides. Set aside.
Heat a large cast iron skillet over high heat for 3 to 4 minutes. Reduce heat to medium and turn skillet upside down over burner. Brush the pan lightly with oil. Place 2 to 3 slices of beef on the pan at a time and sear for 10 seconds on each side. Remove to an ovenproof platter and keep in warm oven. Repeat until all of the beef has been cooked. Serve immediately.