Preheat the oven to 375 degrees F, line a cookie sheet with parchment paper, set aside.
In a large bowl using a hand mixer or stand mixer with paddle attachment combine butter and powder sugar on low until smooth and creamy, about 2 minutes. Add egg and egg white along with vanilla and and peppermint and mix on medium speed until fluffy and well combined, making sure to scrape down the edges as you go, about 3 minutes.
Add the flour and salt and mix on low until fully blended. Divide the dough in half and wrap one half in plastic wrap and shape it into a disc. To the second half add 3-4 drops of red food gel and knead until fully colored, wrap it in plastic wrap and refrigerate both dough discs for 1 hour or overnight, the longer you chill it the better.
Place the dough on a lightly floured surface, roll a tablespoon of each dough (white and red) into a 4- 6 inch long rope. Place the ropes side by side and carefully twist together; curving the end down resembling a cane, add to a cookie sheet lined with parchment paper, repeat with the remaining dough. Brush with beaten egg white and transfer to the preheated oven and bake for 8-10 minutes until firm and golden around edges. Remove candy canes from cookie sheets promptly and transfer to a wire rack with a large spatula.
While the cookies cool, combine crushed peppermint candy and sugar, mixing well. Coat the cookies with candy mixture and allow them to cool completely.
Devour
Notes
Keep uneaten cookies sealed in an airtight container at room temperature for up to 1 week.