Preheat the oven to 350° F and line cookie sheets with parchment paper.
In a medium bowl, whisk together flour, cocoa powder, baking powder, baking soda, espresso and salt. Set aside.
In the bowl with a stand mixer (or using a hand mixer), combine the butter and sugar. Beat on medium-high speed until light and fluffy, 2 to 3 minutes. Add the egg and peppermint extract. Beat until combined, 1 minute. Scraping down the side of the bowl as needed.
With the mixer on low, slowly add the flour mixture and stir until just incorporated. Stir in the chocolate chips.
Scoop a heaping tablespoon of dough, roll into a ball. Slightly flatten the ball and press the top of the dough into crushed candy cane bits. Repeat with remaining dough and place on prepared cookie sheet 1 1/2 inches apart.
Bake 10 to 12 minutes, until edges are firm and the center is still soft. Let cool on the cookie sheets 5 to 10 minutes, then transfer to a wire rack to cool completely.