In a saucepan, combine half the hot water, milk, star anise, cinnamon, cloves, and nutmeg and simmer over low flame until the liquid has reduced by half. Be careful it does not over-boil.Once reduced, sieve and discard solids.
Step 2: Dissolve cocoa powder
In the meantime, dissolve the cocoa powder in the remaining hot water. Add sugar to taste to the hot cocoa mixture.
Step 3: Cool liquids
Let the hot milk mixture and cocoa powder mixture cool to room temperature.Add vanilla extract to the milk.
Step 4: Combine and serve
Once everything has cooled, pour the same amount of the cocoa water into each of the four short glasses.Add ice to the glasses and pour equal amounts of milk into each.