Combine the milk, sugar, cinnamon stick, and salt in a saucepan.

Cook over medium heat, stirring, until the mixture boils and the sugar dissolves.

Whisk the egg yolks in a large bowl.

Slowly pour the warm milk mixture into the yolks, whisking constantly.

Pour the mixture back into the pot.

Cook over medium-low heat, stirring continuously, until the mixture thickens and coats the back of a spoon.

Strain the mixture through a fine-mesh sieve.

Add the heavy cream and stir until well incorporated.

Stir in the brandy or rum and vanilla extract.

Let cool over an ice bath, stirring occasionally.

Refrigerate for a few hours.

Divide the mixture among paleta molds (or glasses).

Freeze until solid (4-5 hours), inserting sticks after 1.5-2 hours if not using molds.