Wash rice in several changes of cold water in a bowl until water is almost clear. Soak rice in cold water 30 minutes (or less if pressed for time), then drain well in a sieve.
While rice is soaking, spread coconut in a skillet and toast over medium heat, stirring occasionally, until pale golden; watch carefully so it doesn't brown too much or burn. Cool completely.
Cook ginger and jalapeno in 1 tablespoon oil in a 4-quart heavy pot over moderate heat, stirring, until jalapeno is softened, about 2 minutes. Add rice and cook, stirring, until fragrant, about 2 minutes.
Stir in water and 1/2 teaspoon salt and bring to a boil, covered. Reduce heat to low and cook, covered, until rice is tender and water is absorbed, 12-15 minutes.
While rice cooks, pulse together coconut, cilantro, scallions, and remaining tablespoon oil and 1/2 teaspoon salt in a food processor until finely chopped.
Remove rice from heat and let stand, covered, 5 minutes. Fluff rice with a fork and transfer to a large bowl.
Add cilantro mixture to cooked rice and stir gently until combined well.