One of my favorite things to cook is rack of lamb. It wows the crowd and -shh- between you and me, it's pretty easy.
Buy your rack of lamb "frenched" and with the chine bone cut. Frenched means the meat is trimmed from the bone ends. The chine bone connects the chops and having it cut means the chops are separate, so you can cut them apart after they're cooked. A full-service butcher department will do these things for you and many packaged racks (such as the vacuum-packed racks from New Zealand) will be prepared this way.
American and New Zealand lamb are both good. American lamb is usually bigger.
Ask the butcher to trim excess fat and the silver skin. If you have to do this yourself, it's not too hard. Begin by trimming most of the fat. You will see a strip of meat with more fat underneath. Trim all of this, saving the removed meat for another purpose. You'll see a tough skin under the fat, called the silver skin. Remove as much of that as you can.
Set the oven to 425 degrees.
Heat a heavy, ovenproof skillet on the stove. (At 425, this means a metal handled skillet). Add a few tablespoons of oil and sear the rack, starting with the meatiest side (where you trimmed the fat), about 5 minutes a side.
While the rack is browning, chop up some fresh rosemary, or use dried rosemary. 4 tablespoons of fresh or 2 of dried should do. Mix with about 1/4 cup of Dijon-style mustard and 2 tablespoons of brown sugar.
Smear the mustard mixture on both sides of the rack and place the pan in the oven. Cook until a meat thermometer shows an internal temperature of 130 degrees (foe medium-rare). This won't take long since you already cooked the lamb much of the way on the stove.
Remove from the oven and cover loosely with foil to let the meat rest of 10 minutes
If you are making two racks, a nice presentation is to lean the two racks against each other with the rib bones intertwined, and carve at the table. Or, you can cut the chops apart and fan out on a platter.