In a saucepan, combine the sugar, cocoa powder, and a tablespoon of water. Heat it over medium heat until the sugar is dissolved.
Stir in the milk and a pinch of salt and continue to heat the mixture. Make sure it doesn't boil; a light simmer is enough.
Stir in the peppermint extract and vanilla extract if desired.
Once the mixture is warm, pour the hot chocolate into your mug and top it with your desired garnishes such as whipped cream, shaved Ande's mint, mini marshmallows, and/or crushed peppermint candies.