In a medium saucepan, combine coconut milk, hazelnut milk, and heavy cream.

Heat over medium-low heat until the mixture is warm but not boiling.

In a separate bowl, whisk the egg yolks and sugar until the mixture is pale and thick.

Slowly add a ladle of the warm milk mixture to the egg yolks, whisking constantly to temper the eggs. Repeat with another ladle.

Pour the tempered egg mixture back into the saucepan.

Cook over low heat, stirring constantly, until the mixture thickens and coats the back of a spoon (about 8-10 minutes).

Remove from heat and stir in nutmeg, cinnamon, vanilla extract, and rum (if using).

Let the eggnog cool to room temperature, then refrigerate for at least 2 hours or until chilled.

Serve in glasses, topped with whipped cream and a sprinkle of toasted coconut flakes.