1: Place the bavette steak in a nonreactive baking dish. Season with kosher salt and sprinkle with bourbon. Place it in the refrigerator to dry-brine for an hour.
2: Make the bourbon butter. Combine the ingredients for the bourbon butter in a small bowl and stir to combine. Place on a square of wax paper or parchment paper and shape into a log. Twist the ends of the paper to enclose the butter. Refrigerate (for up to 5 days) or freeze (for up to 3 months).
3: Remove the bavette from the refrigerator, blot it dry, and paint it with olive oil. Season with freshly cracked black pepper and additional kosher salt.
4: Heat your grill to high. Brush or scrape the grill grates clean and oil with vegetable oil. Place the bavette steak on the hot grill and add the bourbon wood chunks or chips. Cook the steak for 90 seconds, then give the steak a quarter turn and cook for another 90 seconds. Repeat on the opposite side.
5: Before removing the steak from the grill, top it with the bourbon butter.
6: Check the steak with an instant-read meat thermometer. Remove the steak from the grill when it reaches 135 degrees for medium (125 degrees for rare).
7: Place the bavette steak on a wire rack set over a sheet pan to rest.
8: Slice thinly against the grain and serve immediately.