In a large mixing bowl beat cream cheese, butter, corn syrup, and mint extract with an electric mixer on medium speed until smooth. Gradually beat in 3 cups of the powdered sugar until combined. Turn mixture out onto a clean surface dusted with remaining powdered sugar and knead until smooth and no longer sticky.
Divide dough into 3 portions. Tint one portion pink and one portion darker pink. Leave one portion white.
Roll each portion into a 15-inch-long rope. Twist ropes together and form into a rope about 3/4-inch wide. Flatten slightly and cut into 3/4 inch pieces. Arrange pieces on a parchment-paper-lined tray. Cover and chill at least 4 hours. Store covered in the refrigerator up to 1 week.