Bring water, sugar, and anise seeds to a boil in a saucepan; lower heat to medium-low. Simmer until thick and syrupy, about 10 more minutes.
Remove from heat and pour through a strainer to separate the seeds out; set syrup aside to cool slightly.
Beat eggs yolks in a large bowl until light yellow; add rum, condensed milk, evaporated milk, and vanilla extract. Stir in syrup mixture until mixture is smooth.
Pour into decorative bottles and seal tightly. Refrigerate for at least 6 hours before drinking, the longer the better.