To make the peppermint simple syrup, heat the water and sugar in a small saucepan until the sugar dissolves and comes to a simmer, stirring occasionally. Add the peppermint extract and set aside.

Place the chocolate syrup and peppermint syrup in the bottom of a mug. Top with the hot espresso and stir well. Fill with hot frothed milk using the classic milk frother and top with a small amount of foam. Add the whipped cream on top and dust with the candy canes. Serve immediately.