Place the softened butter and powdered sugar in the bowl of a stand mixer fitted with the paddle attachment (or use a large bowl with a hand mixer). Beat on medium speed until the mixture is fluffy and resembles frosting. Scrape down the sides of the bowl.

Add the egg, vanilla extract, and peppermint (or almond) extract. Beat until fully combined, scraping the sides of the bowl as needed.

Reduce the mixer speed to low. Gradually add the all-purpose flour and kosher salt. Mix just until no streaks of flour remain. Use a spatula to fold in any remaining dry bits.

Divide the dough in half. Remove one half and set aside. To the remaining half, add red food coloring and knead or mix until evenly tinted. Adjust the coloring as needed for a vibrant red. Shape both portions of dough into 1-inch thick discs, wrap in plastic wrap, and refrigerate for at least 1 hour (up to 3 days).

When ready to bake, preheat the oven to 375°F (190°C). Line two baking sheets with parchment paper or silicone mats. Pinch off walnut-sized portions (approximately 2 tablespoons) of each dough color. Roll each into a rope about 6 inches long. Place one red rope and one plain rope side by side, press together at the top, and twist to form a spiral. Curve the top into a candy cane shape. Arrange on the prepared baking sheets. If the dough becomes difficult to handle, return it to the refrigerator to chill briefly.

Place the shaped cookies on the baking sheets in the refrigerator for 15 minutes to help them hold their shape.

Bake for 10–12 minutes, until the edges are lightly golden. Allow the cookies to cool on the baking sheets for 10 minutes, then transfer to a wire rack to cool completely.