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.
This recipe contains raw eggs. We recommend that pregnant women, young children, the elderly, and the infirm do not consume raw eggs. Learn more about egg safety from our article, Making Your Eggs Safe.