I have had my problems cooking lamb racks in the past. They turned out either too rare, or overcooked. Then, finally after a lot of trial and error my last 3 attempts at cooking lamb rack were very successful. I got the result I wanted; perfectly cooked juicy medium-rare rib chops and a nicely seared crust. One of the keys to success was using a cooking thermometer the last few times to keep tabs on the doneness of the meat (I hardly ever use one). My target temperature was 135 degrees Fahrenheit, and using a thermometer helped me achieve the perfect results. Here is my recipe for a perfectly cooked rack of lamb, enjoy!

1 rack of lamb,   (have your butcher “French” them for you if you do not know how to do so)
1/4 cup olive oil, plus 1 Tbs separated
2 tsp fresh rosemary, finely chopped
2 tsp fresh thyme, finely chopped
2 cloves garlic, minced
2-3 mint leaves, finely chopped (optional)
2 tsp fresh lemon juice
salt and freshly cracked black pepper
meat thermometer

Directions:

Combine the 1/4 cup of oil, fresh herbs, garlic, lemon juice, salt and pepper into a bowl and whisk together until well mixed. Carve any excess fat from the meat, not all of it since the fat will help flavor the meat. Pour the mixture into a plastic storage bag along with the lamb coating the meat, and remove as much air as you can from the bag, then refrigerate for at least 4 hours or overnight.
Pre-heat your oven to 425 degrees F. Remove the lamb from the bag, shaking off any excess, then discard the marinade. Heat the remaining oil over medium-high heat in a cast iron pan or heavy bottomed skillet until it is smoking hot. Quickly sear the lamb on all sides until a nice crust forms, then put the skillet in the oven for 7-10 minutes or until the thermometer reads 135 degrees F at the thickest part of the meat for medium-rare. Remove the lamb from the pan and allow it to rest 5-7 minutes before carving. Bon Appetit!