Place a grill pan over medium-high heat or preheat a gas or charcoal grill.
In the bowl of a food processor, combine the balsamic vinegar, garlic, honey, and parsley. Pulse until blended. With the machine running, slowly pour in the vegetable oil until the mixture is smooth and forms a thick sauce. Season with salt and pepper, to taste. Reserve in a small bowl.
Season the lamb chops with salt and pepper. Drizzle with the olive oil and sprinkle with rosemary. Grill the lamb chops for 2 to 3 minutes each side until medium-rare.
Arrange the lamb chops on a platter. Spoon the sauce over the top or serve the sauce on the side.
Recipe courtesy of Giada De Laurentiis