For the cocoa mix, stir cocoa powder, sugar, and chopped chocolate. Store in an airtight container.
To make cocoa, heat the milk and cocoa mix in a saucepan over low heat. Stir until chopped chocolate is melted, cocoa mix is dissolved, and milk is hot but not boiling. Pour into a mug and stir in Kahlua. Garnish with marshmallows, if desired.