Combine the cocoa, sugar, and salt in a saucepan. Stir in the boiling water and bring mixture to a boil.
Stir for about 2 minutes. Add milk and heat, but don't bring to a boil. Stir in the chocolate until melted
Divide into serving portions and divide the half and half between them. This late addition brings the cocoa down to drinking temperature.
Remove from the heat and stir in the vanilla.