Position a broiler pan 4 to 6 inches from the broiler and heat. Brush the chops lightly with some of the olive oil and season with salt and pepper. Carefully lay the chops on the hot pan and broil, turning once about halfway through cooking; 7 minutes for rare, 8 for medium, and 9 for well-done. Remove from the oven and set aside for 5 minutes.
Divide the chops between 2 plates and spoon about 1 tablespoon of pesto over each chop; serve.
Mint Walnut Pesto:
Preheat the oven to 350 degrees F. Spread the nuts in a single layer on a baking sheet. Bake for about 8 minutes, shaking occasionally to brown evenly. Let cool.
In a food processor, puree the nuts, mint, parsley, cheese, garlic, and salt. With the motor running, drizzle in the olive oil until incorporated. Transfer the pesto to a container, place a piece of plastic wrap on the surface, and refrigerate for up to 3 days.