1: Heat a heavy dry skillet to medium high. Toast the fennel seed, cumin seed, coriander, and black peppercorns until fragrant, 1 to 2 minutes. Let the spices cool, then pulse them in a spice grinder to create a coarse texture. Add the salt and mint. Store any leftover rub in an airtight container. Use a mortar and pestle if you do not have a spice grinder. Be careful if you use a food processor; it might grind the spice too fine.
2: Make the chimichurri: Mix the mint, parsley, oregano, shallot, garlic, lemon zest, lemon juice, salt, and pepper in a bowl. Once thoroughly mixed, stir in the olive oil. Taste and re-season as needed. Set aside.
3: Set up your grill for indirect grilling and heat it to 400 degrees. Add cherry or apple chunks or chips to the coals or into your smoker box to create wood smoke.
4: Using a sharp knife, score the top of the rack of lamb with a crosshatch pattern. Paint the rack of lamb on both sides with Dijon mustard. Generously season the rack of lamb with the toasted spice rub.
5: Brush or scrape the grill grate clean and oil well. Place the rack of lamb on the grill grate and cook until it develops a crust, about 20 minutes. Add the 1 tablespoon of fresh mint to the butter. Baste the rack of lamb with the butter and mint mixture. Cook the lamb until it reaches an internal temperature of 135 degrees, 25 to 30 minutes, for medium-rare. Optional: Use a bundle of fresh mint as a basting brush.
6: Let the rack of lamb rest for 10 minutes, then slice into individual chops and top with the chimichurri.