Both the mustard-brown sugar glaze and the carrot-ginger essence can be made 2 days ahead of time and held, covered, in the refrigerator.
Preheat the oven to 400°F. Fire up the broiler or grill.
Season the racks of lamb with salt and pepper and grill or broil, turning, until crisp and slightly charred on the outside, 5 minutes on each side. Remove from the grill and set aside.
Put the carrot juice in a medium saucepan and cook over medium heat until reduced by half. Remove from the heat. Whisk in the creme fraîche. Add the ginger and
Combine the brown sugar and mustard in a bowl; blend well. Brush the racks with this mustard-brown sugar glaze and put them in a roasting pan, fat side up. Roast for 10 to 12 minutes.
Meanwhile, finely chop enough of the pistachios to yield
Reheat the carrot sauce. Slice the racks into individual chops. Place them in the center of each of 6 heated plates and splash the carrot sauce around the lamb. Garnish with the remaining whole toasted pistachio nuts.
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