Soak tapioca in coconut water overnight in a bowl covered with plastic wrap.
In a medium lidded pot, combine tapioca–coconut water mixture, coconut milk, vanilla and salt. Cover, bring to a boil, then reduce to a low simmer. Cook, covered, for 40 minutes.
In a bowl, whisk egg yolk and sugar. Slowly whisk in half the tapioca; pour contents from bowl into pot. Cook another 10 minutes over low heat, until thickened. Remove from heat and cool 10 minutes.
Meanwhile, puree 1 cup of the mango in a blender or food processor. Mix into remaining 1 cup mango.
In each of 6 cups, layer 1/4 cup mango, followed by 1 heaping tbsp coconut, 1/2 cup tapioca, another 1/4 cup mango and another 1 heaping tbsp coconut. Cover and refrigerate until cool, at least 2 hours.