Stir the milk and white chocolate together in a medium saucepan. Cook over medium heat, stirring occasionally, until the mixture comes to a simmer and the chocolate is melted. Do not let it come to a boil or let the chocolate burn the bottom.
Remove from heat and stir in vanilla and peppermint extracts.
Serve warm with additional toppings as desired.
Recipe by The Thrifty Couple at https://thethriftycouple.com/10-minute-stovetop-creamy-peppermint-white-hot-chocolate-recipe/