Combine milk, heavy cream, peppermint schnapps (if using), and powdered sugar in a medium saucepan. Over medium heat, bring the mixture to a light simmer, stirring occasionally.

While the milk is heating up, add the chopped chocolate to a microwave-safe bowl and melt in the microwave at 30-second intervals, stirring between each one.

Once the milk mixture has come to a simmer, remove it from the heat. Whisk in the melted chocolate until the hot chocolate is well combined. Serve in mugs topped with whipped cream and/or mini marshmallows.