- 8 1/4 cups water
- 2/3 cup large (3/4- to 1/4-inch) pearl tapioca (not quick-cooking)
- 1/2 cup grated or crumbled dark palm sugar (4 oz)
- 2 (13- to 14-oz) cans unsweetened coconut milk (do not shake)
- 2 firm-ripe mangoes (1 1/2 lb total), peeled, pitted, and cut into 1/4-inch pieces
- 1 lb firm-ripe papaya (preferably red), peeled, seeded, and cut into 1/4-inch pieces
- 1/2 pineapple, peeled, cored, and cut into 1/4-inch pieces
- 2 cups shaved ice
- Garnish: fresh coconut shavings, toasted
- Special equipment: an ice shaver, preferably manual
- Bring 8 cups water to a boil in a 2-quart saucepan and add tapioca, stirring constantly. Gently boil, stirring occasionally, until tapioca is almost completely translucent, 40 minutes to 1 1/2 hours, depending on size of tapioca.
- Remove from heat and let tapioca stand, covered, until completely translucent, 45 minutes to 1 1/2 hours, depending on size.
- While tapioca is standing, bring sugar, a pinch of salt, and remaining 1/4 cup water to a simmer in a small heavy saucepan, stirring until sugar is dissolved. Simmer syrup until slightly thickened, about 5 minutes.
- Scoop out 3/4 cup (total) of thick layer of coconut cream from tops of cans (reserving remainder for another use) and whisk into syrup until combined well. Chill syrup until cold, about 1 hour.
- Add 3 cups cold water to translucent tapioca, then drain in a sieve. Transfer tapioca to a large bowl filled halfway with cold water, swirl, and then drain in sieve. (This removes excess starch.)
- Spoon 3 tablespoons syrup into each of 4 glasses (there will be some left over), then divide fruit and tapioca among them. Top with shaved ice.