Fill 6 compartments of an ice cube tray with water; place a cinnamon stick in each filled compartment; freeze until solid.
In a small saucepan, simmer the coffee, star anise and the remaining 2 cinnamon sticks over low heat for 5 minutes. Stir in the condensed milk and refrigerate until cool.
Strain the coffee mixture and discard the spices. Fill 6 glasses halfway with ice cubes, pour in the coffee mixture and serve with the cinnamon ice sticks.