In a mixing bowl, cream together butter and powdered sugar using an electric mixer until light and fluffy, about 2-3 minutes. Add egg, vanilla extract, and peppermint extract, mixing until smooth.

In a separate bowl, whisk together flour and salt. Gradually add this dry mixture to the butter mixture, stirring until a soft dough forms.

Split the dough into two equal portions. Leave one half plain and add red gel food coloring to the other half, mixing until color is evenly distributed. Wrap both portions and chill in the refrigerator for at least 1 hour.

Preheat your oven to 180°C (350°F) and line baking sheets with parchment paper. Remove chilled dough, roll portions into ropes, twist together and shape into candy cane forms on the baking sheets.

Bake in the preheated oven for 8-10 minutes, or until set but not browned. Cool on baking sheets before transferring to a wire rack.