Beat butter and powdered sugar together until light and fluffy, about 2 minutes.
Mix in flour, salt, and extract just until combined.
Add food color a few drops at a time until desired color is achieved. Stir in peppermint baking chips.
Refrigerate dough, covered, for at least 30 minutes.
Preheat oven to 375 degrees. Line a large baking sheet with parchment paper or silicone baking mat.
Scoop out one tablespoon of dough at a time and form into a ball. Place on prepared sheet.
Bake for 7 to 8 minutes. You do not want the cookies to get more than very lightly browned on the bottom. Let cool for 5 minutes on the baking sheet.
Line another large baking sheet with parchment paper and dust liberally with powdered sugar.
Place slightly cooled cookies on this baking sheet and dust with additional powdered sugar. Let cool completely.
Fill a small bowl halfway with powdered sugar. Drop cookies one at a time into the bowl and turn until coated in powdered sugar.
Store in an airtight container for up to 4 days.