01 - In a medium saucepan over medium heat, combine the whole milk and heavy cream. Warm until steaming but avoid boiling.
02 - Add semisweet chocolate chips, unsweetened cocoa powder, and granulated sugar. Whisk continuously until the chocolate has melted and the mixture is uniform.
03 - Stir in freshly brewed espresso (or strong coffee), peppermint extract, and vanilla extract. Continue heating for 1 to 2 minutes while stirring steadily until the beverage is hot.
04 - Pour the hot chocolate into mugs. Optionally, garnish with whipped cream, crushed candy canes, and chocolate shavings. Serve immediately.