In a medium bowl, combine the chicken with 1 tablespoon cornstarch and 1 tablespoon soy sauce. Marinate for 15 minutes.
In a separate small bowl, whisk together the chicken broth, remaining 2 tablespoons soy sauce, hoisin sauce, sesame oil, sugar, and 1 teaspoon cornstarch to create the sauce.
Heat 1 tablespoon of oil in a wok or large skillet over medium-high heat. Add the cashews and toast for 1-2 minutes until golden brown, then remove and set aside.
Add the remaining oil to the wok. Add the chicken in a single layer and cook undisturbed for 2 minutes, then stir-fry until fully cooked through, about 3-4 more minutes.
Add the bell pepper, garlic, and ginger to the wok. Stir-fry for 2 minutes until the pepper is tender-crisp.
Pour the sauce mixture into the wok. Cook, stirring constantly, for 1-2 minutes until the sauce thickens and glazes the chicken.
Stir in the toasted cashews and green onions. Remove from heat and serve immediately.