Remove the steak from the refrigerator at least 45 minutes before grilling so it comes closer to room temperature. Pat the steak very dry with paper towels.
Rub the steak on all sides with the olive oil, then season both sides and the exposed fat with the kosher salt and freshly ground black pepper.
Prepare the grill for two-zone cooking: one side set to medium-low for indirect heat and the other side set to high for direct searing. Place the steak on the indirect side with the bone toward the cooler zone, close the lid, and cook, turning occasionally, until the internal temperature is about 10°F/6°C below your desired final doneness: 110°F/43°C for rare, 120°F/49°C for medium-rare, or 130°F/54°C for medium. For a 2½- to 3-pound tomahawk this typically takes 20 to 40 minutes, depending on grill temperature and steak thickness.
Move the steak to the high-heat side and sear directly over the flames or hot grates 1 to 2 minutes per side, including the exposed fat and bone, until the surface is deeply browned and the thermometer reaches your final target temperature.
While the steak rests, combine the softened butter, minced garlic, parsley, thyme, and lemon zest in a small bowl and stir until blended and spreadable.
Transfer the steak to a cutting board, tent loosely with foil, and let rest for 10 minutes. Slice the ribeye across the grain into thick cuts and serve with generous slices or dollops of the garlic herb butter.