In small bowl, combine ingredients for herb butter. On a piece of aluminum foil, shape into a 6-inch square. Freeze until firm, about 40 minutes.
While butter is freezing, flatten chicken by placing each piece smooth side down on a sheet of waxed paper; cover with second sheet, and using mallet or side of a saucer, pound until 1/4" thick. Be careful to not break the meat.
Cut frozen butter into 12 squares. Place one square in center of each piece of flattened chicken. Fold long sides over butter; fold ends over and secure with toothpick. Make sure ends overlap and are sealed.
Roll each piece in flour. Dip in beaten egg; roll in crumbs, coating evenly.
Shape each piece into a triangle, using palms of hands. Cover and refrigerate until chilled, about 1 hour.
Deep fry 3 at a time in 3-inch deep, 360°F oil, turning with tongs, until browned, about 5 minutes. Remove from pan and drain, being very careful to not pierce coating.
Keep warm in 200°F oven on pan lined with paper towels for no longer than 15 minutes while cooking remaining pieces.