Pre-heat oven to 350 degrees and line a 12-cavity cupcake tin with papers.
In a large bowl, whisk together flour, cocoa powder, baking powder, baking soda, and salt.
In a medium bowl, add both sugars, buttermilk, vegetable oil, egg, and vanilla. Use a spatula or wooden spoon to stir together until well-combined.
Add wet mixture to dry mixture, stirring until just combined, taking care not to over-mix.
Pour boiling water into bowl and fold until just combined (mixture will seem watery at first). Again, try not to over-mix the batter.
Using a cookie scoop or spoon, fill each cupcake paper with batter about ¾ of the way full.
Bake for 15-18 minutes, until a toothpick inserted into the center comes out clean. Let cupcakes cool in the tin for a few minutes before moving to a baking rack to cool completely.
Once cooled, slice cupcakes in half horizontally. Pipe peppermint frosting onto the bottom half and replace the top half (you could also spoon frosting on if you don't want to pipe). Sprinkle crushed candy canes around the edges to stick to the frosting. Pipe a little frosting on the top of the cupcake and sprinkle some more crushed candy cane.