Combine the sugar and cocoa in a medium saucepan. (I always mix cocoa with the sugar in a recipe to get rid of all the lumps.) Put it over med-high heat and stir in 2 cups water. (Make some of that water coffee if you want, or stir in a teaspoon of instant coffee or espresso – it will intensify the chocolate flavor without adding fat.) Bring to a simmer and cook for about 2 minutes. Take it off the heat and stir in the chocolate. Stir until it melts, or better yet, until it kinda melts but leaves some chunks.
Let the mixture cool, then refrigerate until it's cold. Pour into the ice cream maker and freeze according to the manufacturer’s directions.
If you want to firm it up, put it in the freezer for a few hours.