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 205 degrees C.
Generously sprinkle the lamb racks with salt and pepper. Heat the remaining 2 tablespoons oil in a grill pan or heavy large frying pan over high heat. Place 1 lamb rack in the frying pan 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.
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.
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 grill. 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, grill 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. 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)