In the bowl of a stand mixer, combine the unsalted butter, granulated sugar, peppermint extract, vanilla extract, baking powder, and kosher salt. Beat the mixture until it forms a paste that clings to the sides of the bowl. Scrape down the bowl as needed. Beat in the egg until fully absorbed. Add the all-purpose flour and mix just until the dough comes together with no visible flour streaks.

Divide the dough in half. Remove one half from the mixing bowl and set aside. To the remaining dough in the bowl, add the red food coloring and mix on low until the color is even throughout. Shape each dough half (plain and red) into a disk, wrap them individually in plastic wrap, and refrigerate for at least 3 hours or overnight until firm.

Line a baking sheet with parchment paper or a silicon baking mat. Working with firm, chilled dough, pinch off a 1-inch round of each dough (plain and red). Roll each into a 5-inch rope, then place them side by side and gently twist together. Curve the top to form a candy cane shape. Arrange on the prepared baking sheet, spacing cookies about 2 inches apart. Repeat with remaining dough. If the dough is too stiff, let it sit briefly at room temperature until malleable, but avoid over-softening.

In a small bowl, beat the egg white with 1 tablespoon water until foamy to create an egg wash. Brush each shaped cookie with the egg white wash and sprinkle sparkling sugar over the tops for a festive touch. I always find that sparkling sugar gives these cookies a beautiful holiday sparkle.

Bake the cookies in a preheated oven at 350°F (175°C) for 8 to 10 minutes, or until the edges are just barely golden. Let the cookies cool on the baking sheet for 10 minutes before transferring them to a wire rack to cool completely. Enjoy when fully cooled.