1. Bring 2 1/2 cups water to a boil over high heat in a 2-qt. saucepan. Stir in the tapioca pearls and cook, stirring occasionally, until the pearls are translucent and the liquid has thickened, about 12 minutes. To check tapioca pearls for doneness, look for a tiny white dot in the center of the pearl; if you don't see one, continue to cook.

2. Add bananas, coconut milk, sugar, and salt and bring to a boil, stirring constantly. Reduce heat to medium-low; simmer, stirring occasionally, until the bananas are just soft and the flavors have melded, about 2 minutes. Remove pan from the heat, stir in the vanilla, and let soup cool for 10 minutes. Ladle soup into small bowls and top with peanuts, if you like.