1. Place mint, parsley, walnuts, and garlic in a food processor. Process until chopped. With machine on, pour 1 cup olive oil through feed tube in a slow stream. Continue to process until pesto is finely chopped but not pureed. Season with vinegar, 3/4 teaspoon salt, and 1/4 teaspoon pepper. Set mint pesto aside.
2. Light a hot fire in a grill or preheat a broiler. Trim excess fat from chops. Season with remaining 1 teaspoon salt, 1/4 teaspoon pepper, and 2 tablespoons olive oil. Grill or broil 3 inches from heat 4 minutes on one side. Turn and cook 2 minutes more, or until cooked to desired doneness. Serve with mint pesto