Place chocolate in a large heatproof bowl; set aside.
In a medium saucepan, whisk together milk powder and cornstarch. Whisk in 1 cup (250 mL) of the milk until smooth; whisk in remaining milk. Heat over medium heat, whisking often, until slightly thickened and steaming hot, about 5 minutes (do not boil).
Pour milk mixture over chocolate; let stand for 30 seconds. Whisk until melted and smooth. Add vanilla and peppermint extract.
Pour into 4 mugs; sprinkle with shaved dark chocolate and serve with peppermint sticks or candy canes on the side for stirring.
Recipe Notes
Per Serving: 279 calories, 12 g protein, 11 g fat (6 g saturated fat), 35 g carbohydrates, 0 g fibre, 17 mg cholesterol, 172 mg sodium