Pat the steak dry thoroughly with paper toweling. Cover with plastic wrap and rest at room temperature for 30 minutes. Liberally salt and pepper both sides of the steak right before grilling.
Meanwhile, prepare your charcoal grill. Light the coals using a chimney starter. When the coals are thoroughly ashed over, dump them into the kettle of your grill on one side for indirect heating. Place the grate on top and clean well.
Place the steak directly over the hot coals. Grill for 1–3 minutes, until the steak develops a nice sear. Flip and repeat on the other side.
Move the steak to the indirect side of the grill (but still close to the coals). Grill, flipping once, until done to your liking (see Recipe Notes #3–4).
When the steak is approximately 5 minutes away from being done, heat a cast-iron skillet over high heat on the stovetop. When the skillet is hot, reduce the heat to medium-high and add the butter. When the butter is melted, tilt the pan to spread the butter and olive oil all around the skillet. Add the onions and mushrooms. Saute, stirring frequently, until the vegetables are softening and turning a light, golden-brown color.
Remove the steak from the grill when it reaches your desired doneness. Rest for a minimum of 10 minutes. Slice the steak against its grain and serve with the mushrooms and onions.