Heat milk (or milk and cream combo) on the stove top in a medium sauce pan.
Bring to a simmer, not a boil.
Stir often so the milk does not burn to the bottom of the pan.
Once the milk has come to a low simmer remove the pan from the heat and add in the chocolate chips.
Stir until all of the chocolate is melted and the drink is creamy.
Stir in 1/2 tsp of the peppermint extract.
Taste and only add more if you need to. Peppermint is a strong flavor.
Serve warm with whipped cream and a candy cane or other optional toppings.