Soften saffron in hot water (2 tablespoons) in a small bowl.
Heat oil in a 5-quart heavy pot over medium-high heat until it shimmers. Fry almonds, stirring frequently, until golden, about 3 minutes. Transfer with a slotted spoon to paper towels to drain.
Fry onion in oil remaining in pot, stirring occasionally, until golden brown, 15 to 20 minutes. Transfer half of onion to a bowl.
Add rice to onion in pot and cook, stirring, until fragrant, about 2 minutes. Add water (4 1/2 cups), saffron mixture, 1 1/2 teaspoons salt, and 1/2 teaspoon pepper and bring to a simmer. Reduce heat to low and cook, covered, until water is absorbed and rice is tender, 18 to 20 minutes. Let rice stand, covered, off heat 5 minutes.
While rice stands, stir almonds and currants into bowl with onion.
Fluff rice with a fork and serve with almond mixture spooned on top.
Rice pilaf can be made 1 day ahead and chilled. Reheat, uncovered, in a microwave or, tightly covered, in a 250°F oven.