In a small mixing bowl whisk together flour, baking powder, and salt.
In a separate larger mixing bowl or in your stand mixer cream together butter and cream cheese until creamy. Add in sugar and continue to mix until light and fluffy. Last add in your egg along with your peppermint extract.
Slowly add your dry ingredients into your mixer with your wet ingredients until well combined. Cover and chill for 1 hours or over night.
Preheat oven to 350 degrees and prepare a baking sheet with parchment paper.
Roll dough into balls (about 2 tablespoons per cookie) and place on your prepare baking sheet. Bake for 14-15 minutes then allow to cool on the pan for 5 minutes before allowing them to cool completely on a rack.
Cream together cream cheese and butter in a stand mixer or with an electric mixer. Once your cream cheese and butter is well combined and creamy add in sugar and peppermint extract and then continue to beat until your frosting is creamy and smooth.
Once cooked are completely cooled spread on cream cheese frosting and top with peppermint crunch baking chips.