- Prepare the cocoa sugar syrup: Put the sugar and cocoa in a saucepan. Use a wire whisk to stir the sugar and cocoa together. Slowly whisk in the water to make a smooth mixture, with no lumps of cocoa remaining. Place over medium-high heat, stir with a wooden spoon and bring to a boil, 3 to 4 minutes. You want bubbles rising and breaking all over the surface. Stirring frequently, boil the syrup until it is dark and smooth and there are no visible grains of sugar, 1 to 2 minutes.
- Add the chocolate to the syrup: Remove the pan from the heat. Add the chocolate and let it stand for 1 minute so that it begins to melt, then stir with the wooden spoon until the chocolate is completely melted and the mixture is smooth and uniformly dark, 1 to 2 minutes. Stir in the vanilla and espresso powder (the espresso powder deepens the flavor) and continue stirring until smooth.
- Chill the chocolate mixture: Pour the chocolate mixture into a bowl, scraping the sides of the pan with a rubber spatula. Let cool to room temperature, 30 to 45 minutes. Cover the bowl with plastic wrap and refrigerate the mixture until it is very cold, at least 3 hours or up to 8 hours.
- Churn the sorbet: Prepare an ice cream maker with at least a 1-quart capacity according to the manufacturer's instructions. Pour the well-chilled chocolate mixture into the ice cream maker and churn. The timing will depend on the type of ice cream maker and the temperature of the chocolate mixture. When the sorbet is almost finished churning and it has thickened and mounds on the paddle, add the liqueur or syrup. Continue to churn until the sorbet is smooth and mounds again, 1 to 2 minutes.
- Serve or store the sorbet: The sorbet can be served immediately, directly from the mixing container, when it is soft and richly flavored. For a firmer consistency, use a rubber spatula to transfer the sorbet to a plastic freezer container. Cover tightly and freeze until the sorbet is firm, at least 3 hours or up to 3 days. The sorbet has a little fat in it from the melted chocolate, so it will keep its texture in the freezer longer than a pure fruit sorbet. It is at its best when served within 12 to 24 hours. Makes about 1 quart.
- Pastry Chef's Tip: Cocoa powder often forms clumps when combined with a liquid. If you mix it with sugar first, however, the cocoa grains will separate and are more likely to remain that way. If the cocoa still clumps a bit after you add the water, keep whisking while you heat the cocoa-sugar syrup and the lumps will eventually dissolve.