Bring the water to a rolling boil in a medium saucepan over high heat. Add the tapioca pearls and stir to separate. Reduce the heat to low and simmer until the tapioca becomes translucent, about 20 minutes. Add the coconut milk, sugar and salt and stir well.
Five minutes before the end of cooking time, peel the bananas and cut them in half lengthwise. Cut each piece again into 4 pieces. Add them to the pan and cook until just soft. At this point the tapioca pearls should be clear and cooked.
Remove from the heat and transfer to individual dessert bowls. Garnish with the peanuts and serve hot or at room temperature. (The pudding will thicken as it cools.)
Recipe courtesy Mai Pham's PLEASURES OF THE VIETNAMESE TABLE (HarperCollins, 2001)