Combine chicken and 2 Tbsp. teriyaki sauce in a bowl and set aside. Warm 1 1/2 Tbsp. vegetable oil in a wok or large nonstick skillet over high heat. Add chicken and cook, stirring, until no longer pink, 3 to 5 minutes. Transfer to a clean bowl.
Add scallions, garlic, ginger and remaining vegetable oil to wok and cook, stirring, until fragrant, about 1 minute. Add snow peas and chicken broth, cover and cook until tender, 2 to 3 minutes. Stir in rice, chicken and remaining 2 Tbsp. teriyaki sauce and cook, stirring, until rice is heated through, 1 to 2 minutes. Sprinkle cashews on top and serve immediately.