Combine chicken and 2 tablespoons teriyaki sauce in a bowl. Heat 1 1/2 tablespoons vegetable oil in a large skillet or wok over high heat. Add chicken; cook and stir until no longer pink in the center, 3 to 5 minutes. Transfer to a separate bowl.
Stir scallions, garlic, ginger, and remaining vegetable oil into skillet until fragrant, about 1 minute. Stir in snow peas and chicken broth; cover and cook until tender; 2 to 3 minutes.
Stir rice, cooked chicken, and remaining teriyaki sauce into skillet; cook and stir until rice is heated through, 2 to 3 minutes. Sprinkle with cashews.