Place the steaks in a single layer on a baking sheet and pat dry with a paper towel. Rub the oil into both sides of the steaks and then season them evenly with the salt. Let stand while you prepare the board sauce and the grill.
Arrange all the board sauce ingredients, including ½ teaspoon of the pepper, in a pile in the center of a large cutting board, putting the oil and vinegar in the center of the pile. Let the pile stand while you preheat the grill and grill the steak, or for up to 1 hour.
Related Grill Skills
Zest a Lemon
Prepare the grill for direct and indirect cooking over medium-high heat (400° to 450°F). Brush the cooking grates clean.
Grill the steaks over direct medium-high heat, with the lid closed, until cooked to your desired doneness, 10 to 12 minutes for medium rare (125° to 130°F), rotating and turning the steaks once or twice. To cook the steaks longer, slide them to the indirect heat side of the grill.
Meanwhile, use a wooden spoon to mix the sauce ingredients together gently on the board into a juicy, chunky mixture.
Spread the board sauce into a layer large enough to accommodate both steaks side by side.
Use tongs to transfer the steaks to the cutting board, laying them flat on the sauce. Season the tops with the remaining ½ teaspoon pepper.
Use the tongs to move the steaks around so they pick up some of the sauce flavorings, then turn the steaks over. Let rest, uncovered, for 3 to 5 minutes.
Cut the meat away from the bone.
Next, cut the meat across the grain into ⅓-inch-thick slices. As you cut the meat, turn each slice back and forth in the board sauce until it is nicely coated with the flavorings. Season with salt and pepper if needed and serve right away.