In a large bowl, beat the eggs until frothy and light.

Mix in the sweetened condensed milk, whole milk, dark rum, vanilla extract, ground cinnamon, ground nutmeg, and a pinch of salt until well combined.

Pour the mixture into a saucepan and cook over low heat, stirring constantly, until the mixture is thick enough to coat the back of a spoon, about 5 minutes. Do not let it boil.

Once cooled, strain the mixture through a fine-mesh sieve to ensure a smooth texture.

Pour into a bottle or pitcher and refrigerate until chilled.

Serve cold in small glasses with a sprinkle of ground cinnamon or nutmeg on top, if desired.