In a medium saucepan, warm about one-third of the half-and-half or milk, with the chopped dark and milk chocolates, stirring until the chocolate is melted.
Whisk in the remaining half-and-half or milk as well as the salt and cinnamon, heating until the mixture is warmed through.
Use a hand-held blender, or a whisk, to mix the hot chocolate until it’s completely smooth. (Do not use a standard blender as blending hot liquid can result in the lid coming off while blending.) While the chocolate is ready to serve now, if you let it sit for a few hours, it'll get richer and thicker the longer it sits.