In a medium saucepan, combine the sugar, heavy cream and 3/4 cup of water and bring to boil over moderately high heat. Off the heat, whisk in the cocoa until smooth. Add the chocolate and stir until completely melted. Pour the mixture into a heatproof bowl and let cool to room temperature, then refrigerate until chilled. Transfer the mixture to an ice cream maker and freeze according to the manufacturer's instructions.
The sorbet can be frozen in an airtight container for up to 5 days.
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