Blend the mint, basil, nuts, cheese, lemon juice, garlic, salt and pepper to taste 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. Add more if needed.

Preheat the oven to 425 degrees.

Generously sprinkle the lamb racks with salt and pepper. Heat the remaining 2 tablespoons oil in a 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 – 25 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. Serve the pesto in a separate bowl with the chops and serve immediately.

The pesto may be made ahead and the racks may be seared ahead and chilled. Remove them from the refrigerator about 30 minutes before roasting so that they don’t go into the oven too cold, as they will take longer to roast.