In your medium saucepan, whisk together the cocoa powder and granulated sugar to prevent clumps.
Slowly pour in the 2 cups of milk and 1/2 cup of heavy cream while whisking continuously to create a smooth base over medium-low heat.
Continue whisking frequently as the mixture heats, keeping it hot but not boiling, for about 3-5 minutes until cocoa and sugar dissolve fully.
Remove from heat and stir in the peppermint extract and vanilla extract for signature flavor and aroma.
Pour the hot chocolate into a mug, top generously with whipped cream, then sprinkle crushed peppermint candies on top for a festive finish.