Whisk the flour, baking powder, and salt together in a mixing bowl.
In a separate bowl or bowl of a stand mixer, beat together the cocoa powder, white sugar, melted butter, and vegetable oil with a paddle attachment. Then beat in the egg and vanilla.
Add the dry ingredients to the wet ingredients and mix until cookie dough forms. Do not over mix. Fold in the chocolate chip
Use a one or two tablespoon cookie scoop to drop the dough onto a baking sheet lined with parchment paper. Press the cookie dough balls down in the gently.
Bake at 350 degrees for 10-12 minutes. Allow them to rest on the baking sheet for 10 minutes to allow them to firm up before transferring to a wire rack to cool.
Peppermint Frosting: Beat the butter then add the powdered sugar and peppermint extract. When your frosting has reached your desired consistency, spread over the top of each of the baked cookies and sprinkle with the crushed candy cane.