In a saucepan, combine half the water, sugar, salt, and cocoa powder. Warm over medium heat, stirring until the mixture is smooth and combined.
Bring the mixture to a full boil while whisking constantly. Reduce the heat to low and let it simmer for thirty seconds.
Remove from the heat and add the vanilla and espresso. Stir well to incorporate the flavors.
Stir in the remaining water. Transfer to a bowl and chill in the refrigerator until cold, about an hour.
When chilled, pour the mixture into your ice cream maker and freeze according to the manufacturer’s instructions.
