In a mixing bowl, combine minced garlic, chopped rosemary, olive oil, salt, black pepper, and Dijon mustard to create the marinade.

Rub the marinade all over the rack of lamb, ensuring it is well coated. Cover and let it marinate in the refrigerator for at least 1 hour, preferably overnight.

Preheat the grill to medium-high heat.

Remove the lamb from the refrigerator and let it sit at room temperature for about 30 minutes before grilling.

Place the rack of lamb on the grill, bone side down, and grill for about 15-20 minutes, turning occasionally, until the internal temperature reaches 130°F (54°C) for medium-rare.

Remove the lamb from the grill and let it rest for 10 minutes before slicing into chops.