Bring water to a boil. In a separate pan, whisk sugar and cocoa together. Pour about a third of the boiling water into pan with cocoa and sugar mixture, whisking vigorously to blend, then pour in the remaining water and continue to whisk. Simmer the cocoa, sugar and water mixture, stirring occasionally, for about 30 minutes, until syrupy.

Put chopped chocolate into a large bowl and pour in about 1 cup of cocoa syrup. Whisk until chocolate is melted. Whisk in remaining syrup. Chill chocolate mixture.

Pour mixture into ice cream maker and freeze mixture according to the manufacturer's instructions.