Combine boiling water and espresso; stir until coffee dissolves. Pour into an ice cube tray; freeze 4 hours or until firm.
Combine sugar and 2 tablespoons water in a small heavy saucepan over medium heat; cook until sugar dissolves. Continue cooking an additional 5 minutes or until golden. Remove from heat; carefully stir in 2 tablespoons water with a whisk (mixture will bubble vigorously). Let cool.
Combine caramelized sugar, milk, and cocoa mix in a blender; process until well-blended. With blender on, add coffee ice cubes, 1 at a time; process until smooth. Add crushed ice; process until smooth. Serve immediately.