For the steak and potatoes: Preheat half of the grill, setting the burners to medium, about 180°C (350°F). Oil the grate.
With your hands, generously coat the potatoes with 2 tbsp (30 ml) of the oil. Season generously with salt.
On a plate, brush the steaks with the remaining oil. Sprinkle with the pepper. Season generously with salt. Let sit out at room temperature while you cook the potatoes.
On the side of the barbecue that is on, place a square of foil and top with the wood chips. On the side of the barbecue that is off, place the potatoes cut-side up. Close the lid. Let smoke for 45 minutes to 1 hour or until the potatoes are tender when pierced with the tip of a knife. Turn the potatoes over. Increase the temperature of the burners to high.
On the side of the barbecue that is off, place the steaks beside the potatoes. Close the lid and let it smoke for 5 minutes. Turn the steaks over and let smoke for another 5 minutes. Remove the wood chips. Grill the steaks on the side of the barbecue that is on for 8 to 10 minutes, turning them over halfway through cooking, until a thermometer inserted in the centre of the meat reads 63°C (135°F) for rare. At the same time, grill the potatoes on the side of the barbecue that is on for 4 minutes or until golden. Remove the potatoes from the barbecue. Place the steaks on another plate and cover with foil. Let rest for at least 10 minutes. On a work surface, thinly slice the steaks.
For the herb butter: Meanwhile, in a food processor, finely chop the shallot, garlic, and herbs. Season with salt and pepper. Add the butter and mix well. Transfer into a small serving bowl.
Serve the sliced steaks and potatoes on plates. Serve with the herb butter. Delicious served with a green salad.