In a small saucepan, mix ¼ cup sugar and ¼ cup water. Heat it over medium heat until the sugar dissolves. Remove from heat, add ⅛ teaspoon peppermint extract, stir, and let it cool.
In the same pan, whisk together ¼ cup cocoa powder, ¼ cup sugar, ¼ cup water, and a pinch of salt on low heat until it thickens. Stir in 2 tablespoons of heavy cream, then let it cool.
Brew two shots of espresso or make ½ cup of strong coffee. Mix it with mocha sauce and peppermint syrup in a mug. Steam and froth the milk. Pour the frothed milk over the coffee mixture.
Add whipped cream on top, and finish with chocolate curls or crushed candy canes. Serve hot!