Add the milk, sugar and cinnamon sticks to a large pot and bring to a simmer at medium low heat.

In the meantime, beat egg yolks and condensed milk in a medium bowl.

Once the milk begins to simmer, add a few tablespoons of the hot milk to the egg yolk mixture and stir well to temper it. Then add it to the hot milk and stir again. Cook on medium low heat, stirring occasionally for about 10 minutes or until it thickens.

Remove the pot from the stove, take out the cinnamon sticks and strain the eggnog through a sieve into a large bowl. This will remove any clumps or cinnamon pieces that may be left in the mixture. Let it cool completely.

Once cool, add the rum or aguardiente (if using) and the vanilla, stir well and refrigerate, preferably overnight before serving. Serve chilled and garnish with ground cinnamon on top.