Pre-heat oven to 350 degrees F. and line baking sheets with parchment paper. Set aside.
In a medium mixing bowl, whisk together flour, cocoa powder, baking soda, and salt. Set aside.
In an electric stand mixer bowl, cream together butter and sugars until light and fluffy. Beat in eggs and vanilla, scraping down the sides and bottom of bowl as needed. Slowly, add in the dry ingredients until combined.
Take a spoonful of dough, roll into ball, and place onto prepared baking sheets. Slightly press down on each dough ball.
Bake cookies for 8-10 minutes. Allow cookies to cool on pan until transferring to cooling rack to completely cool.
Candy Cane Buttercream
Pour milk into a small bowl or glass and place broken candy cane pieces inside. Let sit until dissolved, stirring occasionally.
Place shortening into a mixer fitted with a paddle attachment. Cream on high for 3-5 minutes, until mixture is soft and slightly soupy.
Add in powdered sugar while mixing on low.
Pour in milk one tablespoon at a time until desired consistency is reached. Beat on high for 3 minutes.