In a medium saucepan, heat the milk until it's hot and bubbles appear. Add salt and the finely chopped dark chocolate and whisk until dissolved and smooth. Bring the hot chocolate to a very low simmer, whisking continuously, and simmer for about 3 minutes (this will thicken it). Stir in the brown sugar if desired and whisk until smooth. Pour into cups and serve with a dollop of whipped cream if desired.
Note: For an even thicker result, make the hot chocolate ahead of time, let it cool and then reheat when ready to serve.