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 gently over medium heat until sugar dissolves.
03 - Increase heat to medium-high and cook without stirring until the mixture reaches 280°F on a candy thermometer, approximately 15 minutes.
04 - Remove from heat and quickly stir in peppermint extract.
05 - Pour half the syrup onto one side of the prepared baking sheet and the other half onto the opposite side. Add red gel food coloring to one portion and mix swiftly with a greased spatula until uniform.
06 - Allow both syrup portions to cool until just cool enough to handle, about 3 to 4 minutes.
07 - Wearing food-safe gloves, pull and fold each portion separately until opaque and satiny, approximately 5 minutes per portion.
08 - Roll each portion into long ropes, twist the white and red ropes together, then stretch gently.
09 - Cut the twisted rope into 5-inch sticks and shape into classic peppermint stick form.
10 - Place the sticks on parchment and let cool completely before storing.
11 - Store peppermint sticks in an airtight container at room temperature for up to two weeks.