Heat the water in a small pot over moderate heat. While waiting for it to boil put the tapioca in a strainer and rinse under cold running water. Stirring often, add the tapioca to the boiling water. Simmer until tapioca is clear, 5 to 7 minutes. Gently stir the tapioca to prevent sticking. Fold in the coconut milk, sugar, salt, and vanilla. Add the bananas and cook only until they are thoroughly hot, 2 to 3 minutes. Sauce should be only thick enough to coat a spoon. If it appears too thick, add a little water or coconut milk. The mixture will be thicker once it cools.
Remove from heat and immediately transfer to Individual dessert bowls. Garnish with peanuts.
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