Cut each turkey breast horizontally from the long side to within 1/2 in. Of opposite side. Open flat; cover with plastic wrap. Flatten into 10 in. X 1/2 in. Rectangles. Remove plastic; top each with 1 teaspoon oil and 1 teaspoon basil. Layer with ham and cheese to within 1 in of edges. Roll up jelly-roll style, starting with a long side. Tie with kitchen string. Place on a rack in a roasting pan.

In a small bowl, combine salt, pepper and remaining oil and basil; spoon some over the turkey. Bake at 325°F for 75-90 minutes of until a meat thermometer reads 170°F. Basting occasionally with remaining oil mixture.

In a blender or food processor, combine the sauce ingredients; cover and process until blended. Cool turkey for 5 minutes before slicing, serve with basil sauce.