In a medium saucepan, combine rice, salt, and 2 1/2 cups water; bring to a boil. Cover; simmer over medium-low heat until rice is tender and water has been absorbed, about 30 minutes. Remove from heat. Spread rice in a single layer over a parchment-lined baking sheet. Let sit, uncovered, 3 to 4 hours.
Bring a medium saucepan of water to a boil. Blanch peas 1 minute. Drain; set aside.
In a small bowl, combine chicken stock and soy sauce; set aside. Heat a wok or a large, straight-sided skillet over high heat until very hot. Add 1 teaspoon oil; swirl to coat bottom and sides. Add shrimp. Cook until shrimp have cooked through, 2 to 3 minutes. Transfer to covered bowl.
In the same wok, swirl in remaining teaspoon oil. Add onion and garlic; cook 2 minutes. Add 3 tablespoons stock mixture as well as ginger, mushrooms, celery, carrot, bell pepper, and black pepper; cook, stirring, 3 minutes. Add 1 tablespoon stock mixture, sprouts, and reserved shrimp; cook, stirring, 1 minute. Add reserved rice and remaining chicken stock; cook 2 minutes. Stir in scallions and blanched snap peas; cook 1 minute more. Stir in watercress, and serve.