In a small saucepan, bring the water to a boil over medium-low heat. Add the hot chocolate mix and espresso powder. Stir until the chocolate is melted and the mixture is smooth. Remove the pan from the heat and stir in the milk.
Place the frozen yogurt and vanilla in a blender. Pour the chocolate mixture into the blender and blend until smooth and frothy.
Pour the shake into 4 (8-ounce) frosted glasses and serve immediately.