In a large bowl, whisk together flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment or in a large bowl with a hand mixer, thoroughly cream butter and sugar until smooth. Add milk, vanilla, peppermint extract and egg and stir to combine.
Stir flour mixture into butter mixture. It is easiest to add the flour in several additions. Be sure to scrape down the side of the bowl between each one.
Divide dough in half. Shape one half into a disk and cover with plastic wrap. Place in the refrigerator.
Place remaining half of dough in the stand mixer and add red food coloring; stir until food coloring is fully incorporated. Shape dough into a disk and cover with plastic wrap. Place in the refrigerator. Chill both sets of dough for at least 4 hours.
Remove dough from the fridge. Take one rounded teaspoonful from the white dough and the red dough. Roll the pieces into thin 4 to 5-inch logs on a silicon mat (for easy counter cleanup). Twist logs together into a candy cane shape and place on baking sheets about 2 inches apart. Repeat with remaining dough.
Preheat the oven to 375°F and line two baking sheets with parchment paper.
Bake cookies for 10-12 minutes or until the centers puff, look matte and have small hairline cracks.
Remove from the oven and sprinkle immediately with crushed peppermint candies. Transfer to the cooling rack to cool completely.