Beat the butter and sugar in your stand mixer until light and fluffy. Add in one egg at a time, then add in coconut milk until thoroughly mixed.
Pour this into a heavy bottom pot and mix in the vanilla bean paste. Stir mixture frequently until temperature reaches approximately 170 degrees and the mixture begins to thicken. It will coat your wooden spoon and leave an edge when you drag your finger though it.
Transfer the pudding to a bowl, cover with plastic wrap to prevent a skin and let cool in fridge.
Serve in individual dishes or store it the fridge until ready to fill your cake.