Salt: Pat the backstrap dry with paper towels. Season evenly with kosher salt. Set on a rack and refrigerate uncovered 1 to 8 hours.
Make the butter: In a bowl, mash the butter with rosemary, thyme, lemon zest, salt, and pepper. Spoon onto plastic wrap, roll into a tight log, and chill until firm. Slice into thin coins and then rest at room temperature. For convenience, simply serve at room temperature as a spread, skipping the rolling and chilling steps.
Rest at room temperature: Set the meat out uncovered at room temperature between 30 minutes and an hour. Pat the meat dry with paper towels.
Preheat the grill: Set up a two-zone fire. Hot side 500 F or higher for searing; cool side for indirect heat. Clean and oil the grill grates.
Final prep: Pat the meat dry again. Lightly brush with oil and season with black pepper.
Sear: Sear over the hot zone for around 2 to 3 minutes per side until well colored.
Finish: Move to the cool side and cook until the center reaches an internal temperature of 120-125°F. Use an instant-read thermometer and probe from the side into the center.
Rest and slice: Transfer to a wire rack or warm platter. And top with a little bit of the butter. Rest 8–10 minutes. Slice across the grain into 1/2-inch pieces on a cutting board.
Butter and serve: Top the slices with more compound butter. Spoon any juices over the meat and serve immediately.