In a large bowl, cream together softened butter and sugar until light and fluffy. Beat in the egg, vanilla extract, and peppermint extract. In a separate bowl, whisk flour and salt. Gradually add the dry ingredients to the wet, mixing on low until just combined.

Divide the dough in half. To one half, add red gel food coloring and mix until the color is uniform. Form both halves into flat disks.

Wrap both dough disks in plastic wrap and refrigerate for at least 1 hour.

Preheat oven to 375°F (190°C). For each cookie, roll one tablespoon of red and one of white dough into 4-5 inch ropes. Place ropes side-by-side, twist them together, and form into a candy cane shape on a parchment-lined baking sheet.

Bake for 9-12 minutes, until edges are lightly golden. Let cool on the baking sheet for 5 minutes before moving to a wire rack to cool completely.