Pour the heavy cream into a small saucepan and warm it over low heat for about 5 minutes, until it starts to simmer gently and you can see steam rising.
Whisk in the cocoa powder, stirring constantly to dissolve any lumps and create a smooth, chocolatey mixture.
Add the sugar and continue whisking until it dissolves completely and the mixture becomes glossy and slightly thickened.
Remove the saucepan from heat and carefully stir in the peppermint extract, releasing a bright, refreshing aroma.
Pour the hot chocolate mixture into mugs, and if desired, top with whipped cream and garnished with candy canes for a festive touch.
Serve immediately while steaming hot, and enjoy the cozy, minty sweetness of this delightful treat.