01 - Preheat oven to 425°F. Pat lamb racks dry with paper towels and season generously with salt and pepper on all sides.
02 - Combine minced garlic, rosemary, thyme, parsley, Dijon mustard, and 2 tablespoons olive oil in a small bowl. Mix thoroughly to form a thick paste.
03 - Rub the herb mixture evenly over the meaty side of each lamb rack, pressing gently to adhere.
04 - Heat 2 tablespoons olive oil in a large oven-safe skillet over medium-high heat. Place lamb racks fat side down and sear for 2-3 minutes until golden brown. Flip and sear the 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 desired doneness.
06 - Remove from oven and tent loosely with aluminum foil. Allow lamb to rest for 10 minutes before carving into individual chops.
07 - Dissolve granulated sugar in hot water. Add white wine vinegar, chopped mint, parsley, and pinch of salt. Stir well and let stand for 10 minutes to allow flavors to develop.
08 - Carve rested lamb between bones into individual chops. Arrange on serving plates and accompany with fresh mint sauce.