Using a sharp knife, cut a deep horizontal slit into each chicken breast to butterfly it. Open each breast so that the chicken lies flat, then cover with plastic wrap and pound with a meat mallet until chicken is 1/2-inch thick. Arrange prosciutto in four piles on a clean surface. Place a slice of cheese in the center of each pile and bring the ends of the prosciutto up around the cheese to create a packet. Lay a prosciutto packet on half of a flattened chicken breast and top with a basil leaf. Fold the other half of the breast over the prosciutto and basil and press down firmly. Repeat with remaining prosciutto packets, chicken, and basil. Transfer flour to a wide, shallow dish and set aside. Season chicken all over with salt and pepper, then dredge each piece in flour, shaking off any excess. Set aside. Heat oil and butter together in a large skillet over medium high heat. Add sage leaves and cook until crisp. Using a slotted spoon, transfer sage to a paper towel-lined plate and set aside. Add chicken to skillet, skin side down, and cook until cooked through and golden brown, about 5 minutes per side. Check for doneness by piercing the thickest part with the tip of a paring knife. If juices are still pink, lower heat and continue to cook another few minutes. Transfer to a warm plate and tent with foil. Deglaze the pan by pouring the wine into it while the pan is still hot. Scrape up the cooked bits and warm until the wine sauce is heated through. Pour over cooked chicken breasts and garnish with fried sage leaves.