Roasted Rack of Lamb with Caramelized Crust

0 Preheat oven to 375ᵒ. In a bowl, mix together the honey, Dijon mustard, chopped thyme, lemon juice, salt and pepper. Set the bowl aside.
1 Brush the lamb with olive oil and season generously with salt and pepper.  Put it in a roasting pan and bake for 12 minutes in the preheated oven. Turn once during this time. 
7 Add the onion, carrot, and garlic to the roasting pan, and roast for 10 more minutes. Once during the 10 minutes, turn and mix the meat and stir the vegetables.
2 Remove the roasting pan from the oven, remove the lamb, and place it in a covered dish with aluminum foil. 
3 Remove all the fat from the roasting pan. Add the wine to the vegetables and boil the liquid for a few minutes, and move the vegetables about with a spoon. When the liquid has been reduced by 1/2, strain it through a sieve into a small pan and keep warm. Press the vegetables through the sieve as well, but do not attempt to push all solids.
4 Meanwhile, preheat the boiler at maximum heat. Place the rack back into the roasting pan, with the meat side up and the bones facing downward. Brush the top rack with the reserved honey mixture. 
5 Put the meat under the broiler for 3 minutes, until the top of the rack is nicely caramelized.
6 Cut the rack into 8 chops, and arrange them in 2 plates with liquid of the roasting pan.