In a medium bowl, combine the chicken, garlic, 1 teaspoon of the soy sauce, 1 teaspoon of the cornstarch, 1 teaspoon of the rice wine, 1/2 teaspoon of the salt, and sugar. Stir to combine.
In a small bowl combine the broth, the remaining 1 teaspoon soy sauce, 2 tablespoons rice wine, and 1/2 teaspoon cornstarch.
Heat a 14-inch (36 cm) flat-bottomed wok or a 12-inch (30 cm) skillet over high heat until a bead of water added vaporizes within 1 to 2 seconds of contact. Swirl in 1 tablespoon of the oil, tilting the wok to evenly coat the bottom of the pan. Add the ginger and, using a metal spatula, stir-fry until the ginger is fragrant, about 10 seconds.
Push the ginger to the sides of the wok, carefully add the chicken mixture, and spread it evenly in a single layer. Cook the chicken, undisturbed, for 1 minute. Then stir-fry until the chicken is lightly browned but not quite cooked through, about 1 minute more.
Swirl the remaining 1 tablespoon oil into the wok, add the sugar snaps, carrots, celery, and cashews, and sprinkle with the remaining 1/4 teaspoon salt. Stir-fry just until the sugar snaps are bright green, about 1 minute. Restir the broth mixture and swirl it into the wok, adding it along the sides rather than into the middle. Stir-fry until the chicken is just cooked through, about 1 minute.
Serve the cashew chicken immediately.