In a large saucepan combine 3 cups (720 ml) of milk, vanilla extract and sugar. Cook over medium heat, stirring occasionally, until the sugar dissolves and milk begins to simmer.
Meanwhile, combine the rest of the milk with ground chocolate powder and cocoa in a small bowl and whisk until smooth.
Add the chocolate mixture to the simmering milk and keep cooking for another 20 minutes on low heat, maintaining a simmer and whisking occasionally to prevent sticking.
Remove saucepan from the stove and let cool to lukewarm. Whisk in the rum. Strain the chocolate liqueur and pour into prepared bottles. Keep it in the refrigerator and use with 2-3 months.
Notes
This recipe makes about 7 cups of liqueur, which is enough to serve at least 15 people. I used rum with the alcohol content of 40% (ABV = 80 proof), you can of course use a lighter or stronger rum, and adjust the amount to your own taste.If you don't have chocolate powder you can use good quality milk chocolate. (Stir melted chocolate into warm milk and follow the recipe.)Because alcohol has a different density than milk the two separate in a bottle. You'll notice that your chocolate liqueur is suddenly of two different colors if it's been standing in the refrigerator for a while. Shake the bottle or simply stir the liqueur with a straw before serving.