Preheat oven to 350 degrees. Lightly grease ramekins with oil.
Beat eggs by hand with a fork or with an electric mixer for 1 minute.
Add the salt, sugar, vanilla and coconut milk and stir until well blended.
Pour a little syrup into the bottom of each ramekin (enough to cover the bottom + up to 1 Tbsp. more).
Now pour egg and coconut mixture into each ramekin until 3/4 full. (Do not stir – syrup will 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 at least 1/4 way up the side of the ramekin.
Bake for 30 minutes, or until a fork inserted into the pudding comes out clean. Allow to cool, then place in the refrigerator until ready to serve.
To serve, run a knife around the inner rim of each ramekin (to loosen 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-style Creme Caramel will keep (covered) in the refrigerator for up to 5 days.