Place 1/2 cup cream, 2 tablespoons sugar, the milk and chocolate in a small, heavy-bottomed saucepan. Cook over medium heat, whisking constantly, until the chocolate has completely melted and is smooth. Remove from heat and stir in the peppermint flavor.
In a small bowl, beat the remaining 1/2 cup chilled cream with a few drops of peppermint flavor (optional) until soft peaks form.
Serve the hot chocolate with whipped cream and a sprinkling of crushed candy canes. Enjoy!
adapted from Bon Appetit