In a bowl, combine the coconut milk, eggs, cornstarch, flour, and salt with a whisk. Set aside.
In a saucepan, bring the sugar and half the water to a boil. Cook until the mixture caramelizes and takes on a golden brown color. Remove immediately from the heat and add the remaining water and the coconut milk mixture.
Bring to boil, stirring constantly with a whisk. Strain. Pour into a bowl and cover with plastic wrap directly on the surface of the pudding. Refrigerate until completely chilled.