01 - In a medium saucepan, whisk together milk, heavy cream, cocoa powder, and sugar over medium heat until well blended and steaming without boiling.
02 - Add semisweet chocolate chips if using and whisk continuously until fully melted and the mixture is smooth.
03 - Remove saucepan from heat and stir in vanilla and peppermint extracts thoroughly.
04 - Pour the hot chocolate into mugs prepared for serving.
05 - Top with whipped cream and sprinkle crushed peppermint candies if desired, then garnish each mug with a peppermint stick.