Place chicken pieces in 2 Tbsp. soy sauce in a deep bowl. Cover and refrigerate for 30 minutes. Remove chicken and drain on paper towels.
Dissolve the cornstarch in the chicken broth and stir in the remaining 1 Tbsp. soy sauce, ginger, and hot sauce; set aside.
Heat half of the oil in a wok or large skillet over high heat. Stir in the chicken; cook and stir until the chicken is no longer pink, about 5 minutes. Remove the chicken from the skillet or wok and set aside.
Pour the remaining tablespoon of oil into the wok/skillet and stir in the onion, broccoli, and water chestnuts. Cook and stir until the chestnuts are hot and the onion has softened, about 5 minutes more.
Stir up the sauce to redistribute the cornstarch, then pour into the mixture and bring to a boil. If if appears too thick, just add water to desired consistency. Add the reserved chicken and stir until the sauce thickens, and the chicken is hot. Stir in cashews and serve over rice.