In a large bowl, use an electric mixer to cream the softened butter and granulated sugar until light and fluffy, about 2-3 minutes. Beat in the egg, vanilla extract, and peppermint extract until well combined.

In a separate bowl, whisk together the all-purpose flour and salt. With the mixer on low, gradually add the dry ingredients to the wet ingredients until just combined. Do not overmix.

Remove half of the dough from the bowl. To the remaining half, add the red gel food coloring and mix until the color is evenly distributed.

Form both the white and red dough into 1-inch thick discs. Wrap each disc tightly in plastic wrap and refrigerate for at least 1 hour, or up to 3 days.

Preheat your oven to 375°F (190°C). Line two large baking sheets with parchment paper.

Take one tablespoon of the white dough and one tablespoon of the red dough. Roll each piece into a 4 to 5-inch rope. Place the ropes next to each other, gently press them together, and then twist. Transfer the twisted rope to the baking sheet and curve the top down to form a candy cane shape.

Bake for 9-12 minutes, until the edges are firm and very lightly browned. If using, sprinkle the crushed peppermint candies over the hot cookies immediately after they come out of the oven.

Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.