Combine the first 6 ingredients in a large shallow non-reactive container. Place lamb in marinade and let marinate in the refrigerator for 2 to 3 hours.
Preheat a grill over medium heat. Remove lamb from marinade and grill lamb racks until desired degree of doneness. Top with the Roasted Garlic Rosemary Butter and serve with the balsamic mint vinaigrette.
Cook the garlic in olive oil in a skillet on the stove for 15 to 20 minutes, or until soft and fragrant. Remove from heat and let cool slightly. Add garlic-olive oil mixture and all remaining ingredients to a food processor and process until thoroughly combined. Keep refrigerated until ready to use.
In a food processor, combine the mustard, mint, shallots, and balsamic vinegar by pulsing a few times. With the food processor running, slowly add the olive oil, and salt and pepper, to taste. Process the mixture again until smooth.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.
Recipe courtesy of Reed Mooney, Shadow's Keep, Missoula, MT