Combine the coconut milk, brown sugar sweetener, and sea salt in a small saucepan. Use a whisk to combine it all and allow the heat to melt the coconut fat.
Once the mixture is starting to simmer, slowly pour the hot mixture into the egg yolks. Whisk vigorously until the yolks incorporate a little bit of the hot coconut milk mixture. Continue to add all the hot coconut milk mixture until combined. Then transfer the mixture back into the saucepan and cook until the mixture starts to simmer again.
Sprinkle in the xanthan gum a little at a time, whisking constantly. Cook until thickened.
Then transfer the pudding to a small bowl, then set it inside of an ice water bath. Continue whisking until the pudding begins to thicken further and cool down. Place the pudding bowl into the fridge to chill. It will continue to thicken as it cools. Serve chilled!