In a large bowl, beat the butter, granulated sugar, and powdered sugar until smooth. Stir in peppermint and vanilla extracts, then add the egg and mix until combined.

Sprinkle in the baking powder, salt, and flour. Mix just until no dry spots remain.

Split the dough into two portions. Mix the red food coloring into one portion until the color is even. If needed, add more food coloring until you reach your desired shade of red.

Shape each portion into a disk. Wrap in plastic and chill in the fridge for at least 3 hours.

When ready, preheat your oven to 350°F and line a baking sheet with parchment paper. Roll about 1-inch pieces from each dough portion into 5-inch ropes.

Pair one red rope with one white rope, twist them gently together, and bend the top into a candy cane shape. Place on the baking sheet, brush with the egg white (beaten with a splash of water), and sprinkle with sparkling sugar.