1. Rub the steak with 2 tablespoons of the olive oil and coat with the thyme. Season with salt and pepper.
2. In a large cast-iron skillet, heat the remaining 1 tablespoon of olive oil until shimmering. Add the meat and pan-fry over moderately high heat until browned and crusty, about 4 minutes per side for medium rare. Transfer the steak to a cutting board and let stand for 5 minutes.
3. Add the shallots to the skillet and cook over moderately high heat, stirring occasionally, until softened and browned, about 3 minutes.
4. Thickly slice the steak across the grain and arrange on plates. Spoon the sautéed shallots on top of the steak and serve immediately.
Notes: If the steak has a membrane that runs down the middle of the meat, remove it by cutting on either side of the membrane, dividing the steak into 2 long strips.