Break the dark chocolate into small pieces and place them in a medium saucepan.
Add the milk and heavy cream. Heat over low heat, stirring constantly, until the chocolate is completely melted and the mixture is smooth. Be careful not to burn it.
Add the granulated sugar and vanilla extract. Stir until the sugar is dissolved.
Allow the mixture to cool to room temperature.
Pour in the vodka and stir thoroughly until you achieve a homogenous consistency.
Strain the liqueur through a clean cheesecloth or a fine-mesh sieve to remove any chocolate particles.
Pour the finished liqueur into sterilized bottles and refrigerate for at least 24 hours to allow the flavors to meld.
Serve chilled, neat or with desserts.
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