Beat the softened butter and confectioners' sugar until light and creamy. Add the egg, vanilla extract, and peppermint extract, then beat until evenly combined.

Gradually mix in the all-purpose flour and salt until a soft dough forms. Divide the dough in half and tint one portion red, leaving the other portion plain.

Cover both portions and chill for 30 to 60 minutes, or until firm enough to shape. If the dough becomes soft while forming the cookies, chill it briefly again.

Roll a small piece of each dough color into a rope approximately 4 inches long. Place the ropes side by side, twist them together gently, and curve one end into a candy cane shape.

Arrange the shaped cookies on ungreased or parchment-lined baking sheets, leaving about 1 inch between cookies. Add optional crushed peppermint candies or red-and-white sanding sugar if desired.

Bake at 375°F (190°C) for 9 to 12 minutes per batch, just until the edges are set and very lightly colored. Do not overbake, because the cookies should remain tender.

Cool the cookies on the baking sheet for several minutes, then transfer them to a wire rack. Let them cool completely before storing or arranging them on a serving platter.