Place each chicken breast half between 2 pieces of plastic wrap. Pound lightly with the flat side of a meat mallet to a rectangle about 1/4 inch thick. Remove plastic wrap. Sprinkle with salt and pepper.
Spoon a slightly rounded tablespoon of the Parmesan Pesto onto each chicken breast half; spread pesto over chicken. Fold in bottom and sides of each chicken breast half; roll up into a spiral. Secure with wooden toothpicks.
Heat butter and oil in a 12-inch skillet over medium heat. Add chicken rolls; cook, uncovered, about 20 minutes or until chicken is no longer pink, turning occasionally for even browning. Remove toothpicks.
Transfer to a serving platter. Garnish with basil sprigs, if desired. Makes 6 servings.
Place lightly packed fresh basil leaves, grated Parmesan cheese, olive oil, and small clove garlic, halved, in a blender or food processor. Cover and blend or process until smooth, stopping as necessary and scraping side of container. Makes 1/2 to 2/3 cup pesto.