Combine the egg whites and powdered sugar and whisk over a double boiler until the mixture feels smooth to the touch.
Transfer the mixture to a bowl and mix at medium-high speed until the mixture has cooled down to room temperature (this can take 5-6 minutes).
When the mixture feels at room temperature, slow the mixer to medium-low and add the butter, little by little. The butter must be at room temperature. When all the butter has been incorporated, add the peppermint extract. 2-3 drops should be enough, but adjust to taste.
When the cupcakes have completely cooled down, pipe the peppermint buttercream over each cupcake. Top with some crushed candy cane for extra colour and flavour.