Combine ½ cup half and half cream with the corn starch and whisk until the corn starch has fully dissolved.
Pour the remaining half and half cream into a pot and set to medium heat. Bring the cream up to a simmer, then add the sugar and whisk until combined.
Add the corn starch mixture and whisk to combine. Remove from the heat and add the chocolate, whisking until smooth.
Pour into your desired mugs and enjoy!