Combine condensed milk, water, and cinnamon stick in a saucepan and bring to a boil over medium-low heat. Continue to boil mixture, stirring constantly, until milk has thickened, about 10 minutes. Remove from heat and allow to cool slightly.
Combine egg yolks and almonds in a blender; blend until smooth. Add warm milk and blend until well combined. Pour egg yolk mixture into the saucepan and bring to a boil over medium-low heat, stirring constantly. Boil for 2 minutes. Remove from heat and fish out cinnamon stick. Add rum in a very thin stream, stirring constantly.
Cool completely, about 2 hours. Pour into a bottle and refrigerate.