Add the light coconut milk and full-fat coconut milk to a large pot set over medium heat. Add the cinnamon stick and bring the coconut milk to a simmer, stirring often.
In a small bowl, whisk the egg yolks with the sugar until smooth. Once the coconut milk is steaming, gradually whisk in about one cup of the hot coconut milk into the egg mixture, then pour into pot with remaining coconut milk, whisking as you pour.
Once the coconut milk is steaming, gradually whisk about one cup of the hot coconut milk into the egg mixture. Once incorporated, pour in the remaining coconut milk, whisking as you pour.
Cook over medium heat, stirring, until the mixture has thickened and coats the back of a wooden spoon, around two to three minutes.
Remove from the heat and strain the mixture through a fine mesh strainer. Stir in the coconut rum and vanilla, cover and chill in the fridge until cold, about two hours. You may also serve this warm if desired.
To serve, ladle the eggnog into mugs and top with toasted coconut. Enjoy!