Preheat an oven to 400⁰F.

Prepare cookie sheets by spraying with baking spray or covering with parchment paper.

Combine the butter and sugar and beat until light and fluffy.

Add the eggs and mix until well combined.

Add the peppermint extract and mix.

With the mixer running, sprinkle in the baking powder and baking soda and mix until combined.

Turn off the mixer and add the flour and mix just until the flour has been incorporated.

Add the crushed candy canes and mix just until evenly mixed in.

Scoop the cookies out into 1 1/2 to 2 tablespoon portions onto the prepared cookie sheets at least 1 inch apart. Roll the dough into balls and using a glass or the bottom of a measuring cup that has been dipped into flour to press the cookies down slightly to form circles.

Place the cookies into the preheated oven and bake for 9 to 10 minutes. As soon as the bottoms begin to turn a light brown, they are done.

Remove the cookies from the oven and allow to cool before icing.

Reserve 2 tablespoons of milk.

Combine remaining ingredients and beat until combined. If icing is too thick, add more milk 1 tablespoon at a time, mixing well between additions until icing is spreadable.

Spread icing over cooled cookies and sprinkle with crushed peppermint if using.