Into a saucepan over medium-high heat, add 1/3 cup of water, three tablespoons of cocoa powder, and three tablespoons of sugar. Stir over heat until the mixture is thoroughly combined without any lumps. Set aside.
Brew a cup of coffee, measure 1/2 cup of coffee, and set aside.
Add 3 tablespoons of the cocoa mixture to a serving glass, then add the coffee, peppermint syrup, and peppermint extract.
Stir in the steamed milk, then top with whipped cream.
Sprinkle with peppermint pieces on top (optional).
Serve.