Combine the coconut cream, milk, and arrowroot starch in a pot and whisk well to combine. Place on the stove and bring to a medium simmer for 2-3 minutes.
To temper the eggs, add the egg yolks to a small bowl. Fill a ladle with the hot coconut cream mixture and slowly stream over the eggs while whisking.
Reduce the heat of the pudding to a lower simmer and pour in the egg mixture. Stir to combine and simmer for another 6-8 minutes to allow to thicken.
Set a fine mesh strainer over a bowl and strain the pudding through the strainer into the bowl, to remove any solids in the pudding.
Add the vanilla to the pudding and stir to combine. Pour the pudding into three small ramekins or pudding cups of your choice. Transfer to the fridge and allow to set (preferably overnight) until it's a thick pudding consistency.