Combine the espresso, sugar, vanilla, and hot water in a blender and stir until the sugar dissolves. Put the ice in the blender and process on high until the mixture is almost completely smooth. Divide the mixture among 4 short glasses.

Place the ice cream in a microwave on high for 15 seconds, until softened. Scoop one ball of ice cream into each glass. With a small sifter, sprinkle each drink lightly with cocoa powder. Serve with a short straw and a teaspoon.