Pour the milk into a small saucepan and warm over low heat, stirring occasionally until it starts to steam, about 3-4 minutes.
Add the chopped dark chocolate to the warm milk, stirring gently with a whisk until the chocolate is fully melted and the mixture becomes smooth and glossy.
Stir in the sugar and peppermint extract, tasting and adjusting the peppermint for a bright, refreshing burst.
Continue to heat gently, stirring until the mixture is hot and well combined, about 2-3 minutes—avoid boiling.
Remove the saucepan from heat and give the mixture a final stir to ensure everything is evenly blended and fragrant.
Pour the hot chocolate into your favorite mugs, filling them to the brim.
Top each mug with a generous dollop of whipped cream and sprinkle with crushed peppermint candies for a festive finish.
Serve immediately while steaming hot, with a spoon or straw, and enjoy the aromatic, creamy, and refreshing sip.