How to Make It
In a medium bowl, whisk the flour with the baking powder and salt. In a large bowl, using an electric mixer, beat the butter until creamy. Add the confectioners' sugar and beat until light and fluffy. At low speed, beat in the peppermint oil and the dry ingredients until a soft crumbly dough forms.
Scrape the dough out onto a lightly floured surface and gently knead about 3 times. Pat the dough into a 6-inch disk, wrap in plastic and refrigerate until chilled, at least 1 hour or overnight. Let the dough stand at room temperature for about 10 minutes before rolling out.
Preheat the oven to 350°. Line 3 baking sheets with parchment paper. On a lightly floured surface, roll out the dough 1/8 inch thick. Using 3-inch cookie cutters, stamp out shapes as close together as possible and arrange them on the prepared baking sheets. Lightly sprinkle the cookies with the crushed peppermints and bake for about 15 minutes, or until golden brown around the edges. Slide the parchment paper with the cookies onto racks to cool completely. Briefly chill the remaining dough, then reroll and repeat.