Let the lamb come to room temperature for about 30 minutes before you are ready to roast. Season the lamb on all sides with salt and pepper, to taste.
Preheat the oven to 350 degrees F.
Heat the oil in a large, heavy-bottomed skillet with a heatproof handle over medium-high heat. Put the rack into the pan, fat side down, and sear it until it is browned, about 2 to 3 minutes. Turn the rack over and sear the other side for 2 minutes. Put the pan into the oven, and roast the lamb until it is medium-rare, or until the internal temperature reaches 125 to 130 degrees F on an instant-read thermometer, about 15 to 20 minutes. Remove the lamb from the oven, cover it with foil, and let it rest for about 10 minutes before slicing into chops. Serve with the Mint Pesto.
Combine all of the ingredients in the bowl of a food processor. Process until the mixture is almost smooth. Taste and adjust the seasonings with salt and pepper, to taste. The pesto may be made 1 day ahead, covered and refrigerated. Bring the pesto to room temperature before serving.