In a large mixing bowl, cream together the softened vegan butter and powdered sugar until light and fluffy.
Mix in the vanilla extract, peppermint extract, and salt until well combined.
Gradually add the all-purpose flour to the wet ingredients, mixing until a stiff dough forms.
Divide the dough into two equal portions.
Add the red food coloring to one portion of the dough and knead until the color is uniform.
Wrap both dough portions in plastic wrap and refrigerate for 30 minutes to firm up.
Preheat the oven to 350°F (175°C) and line two baking sheets with parchment paper.
For each cookie, take approximately 1 tablespoon of plain dough and 1 tablespoon of red dough.
Roll each piece into a thin rope about 4 inches long.
Place the two ropes side-by-side, twist them together, and curve the top to create a cane shape.
Place the cookies on the prepared baking sheets, spaced 2 inches apart.
Bake for 9 to 11 minutes or until the edges are just set but not browned.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.