1. Place the chicken breasts on a film-covered cutting board and cover with plastic wrap. With a meat mallet, gently pound the breast to an even thickness, approximately 1/3 inch.
2. Remove film from breasts and season with salt and pepper. Cut the Pesto Butter into 8 1-ounce long pieces. Place one piece of butter on each breast. Beginning with the buttered edge, roll each breast until butter is covered. Fold the ends of the breast toward the center and continue rolling. Cover and refrigerate for about 15 minutes.
3. Bread the stuffed breasts using the standard breading procedure with the flour, egg and bread crumbs. Refrigerate for 15 minutes.
4. Fry the breaded breasts in a deep-fry at 325°F until golden brown and fully cooked, approximately 10 minutes.
5. Gently remove breasts from fryer and serve immediately. Garnish with pistachios, garlic and Parmesan cheese.