Place the brown sugar, water, and salt in a heavy saucepan and cook over medium heat.
Cook until the caramel is very dark, bubbling and thick, about 7-10 minutes.
Carefully add the 1 cup of the half and half to the caramel.
The mixture will seize up at first, but keep whisking and it will smooth out.
Allow the mixture to slowly heat up to just under the boiling point.
In a large bowl, whisk together the remaining 1-cup half and half, egg, egg yolks, and cornstarch.
Pour the mixture, in a steady stream, into the caramel, while whisking constantly.
Slowly cook the custard, whisking, and alternating with a wooden spoon, scraping the bottom of the pan, as the custard thickens.
Once the custard is thick, remove the pan from the heat and add the butter and rum.
Strain the custard through a fine strainer if you notice lumps that might have formed, and portion the custard into 4 ramekins or small jars and cover and chill for at least 3-4 hours.
Serve with whipped cream or top with chocolate ganache.
To top with the ganache, pour the hot chocolate mixture on top of set custard and chill before serving.
Garnish with organic blackberries.