Beat eggs with a fork or with an electric mixer for 1 minute.
Add the salt, sugar, vanilla or pandan paste, and coconut milk. Stir until well combined. (If you are using pandan essence/paste, note that it will turn the dessert a bright tropical green.)
Pour a little syrup into the bottom of each ramekin: enough to cover the bottom, plus up to 1 tablespoon more.
Now pour the egg and coconut mixture into each ramekin up to 3/4 full. Do not stir: the syrup should naturally remain at the bottom of the ramekin.
Place ramekins in a large glass baking dish or on a deep-sided roasting pan. Pour some water into the bottom of the baking dish or pan until water reaches 1/4 way up the side of the ramekin.
Bake 30 minutes, or until an inserted fork comes out clean.
Allow to cool, then place in the refrigerator until ready to serve. (Note: you can also serve this dessert warm—it's delicious both ways!)
To serve, run a knife around the inner rim of each ramekin to loosen the pudding. Overturn the ramekins onto individual dessert plates. The pudding should fall out easily, with the syrup naturally dripping down over the coconut custard.
Thai Creme Caramel will keep (covered) in the refrigerator for up to 5 days.