01 - Preheat oven to 425°F. Pat lamb racks dry with paper towels and season generously with kosher salt and freshly ground black pepper on all sides.
02 - In small bowl, combine minced garlic, chopped rosemary, thyme, parsley, Dijon mustard, and 2 tbsp olive oil. Mix thoroughly to form a spreadable paste.
03 - Rub garlic herb paste evenly over the meaty side of each lamb rack, pressing gently to adhere.
04 - Heat 2 tbsp olive oil in large oven-safe skillet over medium-high heat. Place lamb racks fat side down and sear for 2-3 minutes until deeply browned. Flip and sear opposite side for 1 minute.
05 - Transfer skillet to preheated oven. Roast for 15-18 minutes for medium-rare (internal temperature 130°F), adjusting time for preferred doneness.
06 - Remove from oven and tent loosely with aluminum foil. Let rest for 10 minutes to allow juices to redistribute throughout the meat.
07 - While lamb rests, dissolve granulated sugar in hot water. Add white wine vinegar, chopped mint, parsley, and pinch of salt. Stir well and set aside for 10 minutes to allow flavors to meld.
08 - Carve rested lamb racks into individual chops between bones. Arrange on platter and serve with chilled mint sauce on the side.