Begin by placing the rack of lamb on a cutting board and using a sharp knife to slice between the bones, creating 8 individual lamb chops. Try to keep each chop similar in thickness so they cook evenly on the grill.
In a small mixing bowl, combine the extra-virgin olive oil, minced garlic, chopped rosemary, kosher salt, and ground black pepper. Stir until the garlic and herbs are well dispersed in the oil and you have a fragrant, cohesive marinade.
Arrange the lamb chops in a shallow baking dish or large plate with a rim. Pour the marinade over the chops, turning each piece so both sides are generously coated. Use your hands or tongs to rub the mixture into the meat for maximum flavor. Cover and refrigerate for about 30 minutes to let the flavors penetrate the lamb.
Preheat an outdoor grill or stovetop grill pan over medium-high heat until hot. Place the marinated lamb chops on the grill and cook for about 3 minutes per side, or until nicely seared and an instant-read thermometer inserted into the thickest part registers around 135°F (57°C) for medium-rare. Adjust the time slightly if you prefer your lamb more or less done.
Once cooked, transfer the chops to a plate and let them rest for a few minutes so the juices redistribute throughout the meat. Serve warm as they are, or pair them with mint apple sauce as a bright, flavorful alternative to classic mint jelly.