To a pan on medium heat, add milk and cream. You can also use just 2 cups of whole milk as well. The addition of heavy cream just makes it richer and creamier.
Chop 4 oz of white chocolate and add that to the milk and cream mixture as well.
Add peppermint extract and vanilla extract (if using). Stir using a wire whisk until the chocolate melts and everything is well combined and the hot chocolate is heated through. There's no need to boil the mixture but heat it up well and then remove the pan from heat.
To make it look festive, take your serving glass and apply a little honey on the rim. Dip the rim into a plate of crushed candy cane, since we applied honey, the crushed candy cane will stick to the rim.
Pour the peppermint white hot chocolate into a serving mug. Top with whipped cream and some more of the crushed candy cane. Serve immediately and enjoy!
Notes
You can skip the vanilla extract if you like. I like using it since it helps in balancing out the peppermint flavor but it is optional.
Using only milk in this recipe is just fine. Adding heavy cream makes the hot chocolate richer and creamier.