Heat up milk in a sauce pot, over medium heat, until hot but not simmering.
Use a fine strainer or a mesh sugar shaker to sift in the cocoa powder to ensure that there are no clumps.
Whisk in the cocoa powder and add chocolate, sugar, and vanilla extract. Slowly continue whisking as chocolate is melts and incorporates into milk.
When milk starts to simmer, lower the heat to medium-low and continue to cook for a few minutes. Make sure to slowly stir from time to time. (Do not let it boil!)
Take off heat and stir in chocolate liqueur and bourbon.
Serve with some marshmallows or whipped cream of top if you wish.