01 - Preheat oven to 425°F. Pat racks dry and season all over with salt and pepper.
02 - Combine garlic, rosemary, thyme, parsley, Dijon mustard, and 2 tbsp olive oil in a small bowl, mixing to form a paste.
03 - Rub garlic herb mixture thoroughly over the meaty side of the lamb racks.
04 - Heat 2 tbsp olive oil in large oven-safe skillet over medium-high heat. Sear fat side down for 2-3 minutes until browned, then flip and sear 1 minute.
05 - Transfer skillet to oven and roast 15-18 minutes for medium-rare (130°F internal), adjusting for desired doneness.
06 - Remove from oven, cover loosely with foil, and let rest 10 minutes before slicing into individual chops.
07 - Dissolve sugar in hot water. Stir in vinegar, mint, parsley, and pinch of salt. Let sit 10 minutes for flavors to meld.
08 - Slice rested lamb into chops and serve with mint sauce on the side.