Line 2 baking sheets with silicone liners. Set aside. In the bowl of a stand mixer add the butter and sugar. Using a paddle attachment, cream the butter and sugar on medium for 3 minutes. The butter/sugar mixture will appear light in color and fluffy. Add one egg at a time, beating directly after adding. After adding each egg, add the peppermint extract, and vanilla to the mixture. Mix on low speed until combined. Add in the red food coloring, on low speed until combined.
In a large bowl add both types of flour, cocoa, baking soda, cornstarch, and salt, and whisk to combine. Slowly add the flour mixture to the butter mixture while the mixer is on low speed. Continue beating the mixture until a soft dough is made. With the mixer on low beat in the white chocolate chips and crushed candy canes, and mix on low until combined. Place the dough in the refrigerator, covered, until chilled for about 20 minutes.
Preheat the oven to 410 degrees. Place the dough on a well-floured surface. Using a rolling pin, roll out the dough to ½ inch of thickness. With a small-sized circle cookie cutter, cut out 24 circles and place them on a baking parchment-covered baking pan. In a small bowl add the sanding sugar and crushed candy canes, and mix to combine. Dip each cookie into the sugar candy cane mixture and lightly press the mixture into the cookie. Place on the baking sheet.
Bake for 10 minutes or until golden brown on the top. Remove the cookies from the oven and let them cool for 5 minutes. Then transfer the cookies to wire racks to cool completely