Preheat oven to 400F degrees.
Pat dry each rack of lamb and season with salt and pepper.
In a 12-inch skillet over medium high heat, add 3 tablespoons of Bellucci EVOO. Working with one rack at a time, add the rack of lamb to the pan, fat side down. Sear the lamb until you have a golden brown crust, about 3 minutes per side. Sear each of the ends as well. Add another 3 tablespoons of Bellucci EVOO to sear the second rack. Transfer the lamb to a rimmed baking sheet and repeat searing the second rack of lamb. Put the baking sheet in the oven and roast for about 20 minutes or until the lamb reaches an internal temperature of 120F for rare and 125F for medium rare.
Remove the pan from the oven and transfer the lamb to a cutting board. Let the lamb rest at least 15 min.
To prepare the mint pesto – in the bowl of a food processor fitted with a metal blade, add the mint, basil, lemon juice, garlic, pine nuts and Pecorino Romano. Pulse several times to blend well. With the motor running, slowly pour the Bellucci Toscano PGI Organic EVOO through the feed tube. Mix until a smooth paste forms. Transfer to a serving bowl.
Slice the lamb into chops and transfer to a platter with the mint pesto on the side or top each chop with a dollop of mint pesto.
A pair of tongs makes it easier to hold and turn each rack of lamb while searing each side as well as the ends.