Blend the mint, basil, nuts, cheese, lemon juice, garlic, 3/4 teaspoon of salt, and 1/2 teaspoon of pepper in a food processor until the herbs are finely chopped. With the machine running, gradually blend in 1/3 cup of oil until the mixture is smooth and creamy.
Preheat the oven to 400 degrees F.
Generously sprinkle the lamb racks with salt and pepper. Heat the remaining 2 tablespoons oil in a grill pan or heavy large skillet over high heat. Place 1 lamb rack in the skillet and cook just until brown, about 3 minutes per side. Transfer the lamb rack meat side up on a heavy large baking sheet. Repeat with the remaining 2 lamb racks.
Roast the lamb in the oven until cooked to desired doneness, about 20 minutes for medium-rare. Transfer the lamb racks to a work surface. Set aside for 10 minutes. Cut the lamb between the bones into single chops. Spread the pesto over 1 cut side of each chop. Arrange the chops, pesto side up, on plates or a platter, and serve.
Alternately, the racks of lamb can be sliced then broiled before serving. To broil the lamb: Use 18 to 24 meaty single lamb rib chops (about 2 1/2 ounces each, from 3 racks of lamb). Preheat the broiler. Arrange the lamb chops in a single layer over 2 heavy baking sheets. Lightly brush the lamb chops with oil and sprinkle with salt and pepper. Watching closely, broil the lamb chops 3 inches from the heat source until cooked to desired doneness, about 3 minutes per side for medium-rare. Spread the pesto over the chops. Arrange the chops pesto side up on plates or a platter, and serve.
Do-Ahead Tip: The pesto and lamb racks may be prepared up to this point 1 day ahead. Cover the pesto and lamb separately and refrigerate. Allow extra time for the chilled lamb to roast. RECOMMENDED WINE #1: Boroli Barolo 1998 REGION/ORIGIN: Barolo, Piedmont GRAPE/VARIETAL: Nebbiolo RECOMMENDED WINE #2: Avignonesi Vino Nobile d'Montepulciano 2001 REGION/ORIGIN: Montepulciano, Tuscany GRAPE/VARIETAL: Sangiovese (Prugnolo Gentile - local clone of sangiovese)