Combine milk and cream in a small pot. Warm, over medium low heat, stirring often, until bubbles begin to form around the sides and wisps of steam rise from the pot.
Reduce heat to low and add white chocolate and vanilla extract. Stir or whisk until chocolate is completely melted.
Pour into mugs and serve immediately with whipped cream and/or marshmallows.
*The amount of white chocolate you use will depend on how sweet you like your hot chocolate, and the sweetness of the chocolate you're using (it can vary by brand). Start with 2 ounces and add additional, to taste.The same applies to the vanilla extract. The quantity will depend on the brand of white chocolate you've used. Some have more prominent vanilla notes than others. Start with 1/2 teaspoon and add to taste.
Add 1-2 tablespoons of Bourbon, Spiced Rum, Kahlua, Irish Cream, Amaretto, or Chambord. Remember that sweet liqueurs will add sweetness to the drink, so if using them, plan on adjusting your white chocolate quantity, to taste.