Add all of the sauce ingredients into a food processor and pulse until well combined. Place the sauce in a glass jar and store in the refrigerator until needed.
Slice the rack of lamb into individual chops. Place the olive oil, garlic and rosemary into a glass baking dish and stir together. Place the chops into the baking dish, coat both sides and marinate for 30 minutes.
Heat a grill on medium-high heat. Place the lamb chops on the grill for approximately 3 minutes each side. Let the chops sit for a few minutes before serving with the mint apple sauce.