01 - Line a large baking sheet with parchment paper and lightly dust with powdered sugar.
02 - In a medium heavy-bottomed saucepan, combine granulated sugar, corn syrup, water, and cream of tartar. Stir over medium heat until sugar dissolves.
03 - Increase heat to medium-high and cook without stirring until the mixture reaches 300°F on a candy thermometer.
04 - Remove saucepan from heat and quickly stir in the peppermint extract.
05 - Pour half of the hot syrup onto a greased or silicone-matted heatproof surface and add several drops of red gel food coloring; leave the other half uncolored.
06 - Using greased spatulas or heatproof gloves, pull and fold each portion until opaque and slightly cooled, approximately 2 to 3 minutes.
07 - Roll each color into ropes about 1/2 inch thick.
08 - Twist one red rope and one white rope together to form stripes, stretch and shape into long, even ropes.
09 - Cut the ropes into 1-inch pieces using greased scissors or a sharp knife.
10 - Allow the candies to cool completely on the prepared baking sheet, then lightly dust with powdered sugar to prevent sticking.
11 - Store in an airtight container at room temperature.