In a small saucepan, combine milk, heavy cream, and sugar.
Heat over medium-low heat, stirring occasionally, until warm but not boiling. Be careful not to scald the milk.
Remove from heat. Chop white chocolate into small pieces before adding it to the pan.
Whisk continuously until chocolate melts completely and the mixture is smooth and creamy.
Pour into a mug. Add marshmallows, whipped cream, or crushed peppermint if desired.