Add the coconut milk to a medium size pot and warm just below a boil. Meanwhile, add the egg yolks to a large bowl along with the tapioca starch and whisk well. Add the maple syrup and whisk to combine. Slowly add the hot coconut milk while whisking fast. If you add the milk to quick the eggs will scramble.
Once all the milk is added, pour everything back into the pot and turn the heat to medium. Cook until the mixture starts to bubble and whisk the entire time, about 7 minutes. The mixture will be thick but slightly loose.
Take the pot off the heat and add the vanilla extract, butter, and whisk well. Allow the pudding to cool to room temperature. The pudding will thicken to desired consistency once cooled down. Enjoy!