In a heavy saucepan, combine the cocoa powder, sugar, water, vanilla, and a pinch of salt: heat the mixture over low heat, whisking, until the cocoa powder is dissolved and the mixture is a smooth paste.
Gradually add the half-and-half and the milk, (both scalded), and simmer hot chocolate, whisking, for 2 minutes.
Stir in the crème de menthe and the crème de cacao.
Note: (For a frothy result, in a blender blend the hot chocolate in batches.)
Divide the chocolate among mugs and top it with the whipped cream and the chocolate.