In a medium bowl, toss chicken with cornstarch until chicken is coated; season with 3/4 teaspoon salt and 1/4 teaspoon pepper.
In a large nonstick skillet, heat 1 tablespoon oil over medium-high heat. Cook half the chicken, tossing often, until browned, about 3 minutes. Transfer to a plate.
Add remaining oil and chicken to skillet along with the garlic and white parts of scallions. Cook, tossing often, until chicken is browned, about 3 minutes. Return first batch of chicken to pan. Add vinegar; cook until evaporated, about 30 seconds.
Add hoisin sauce and 1/4 cup water; cook, tossing, until chicken is cooked through, about 1 minute. Remove from heat. Stir in scallion greens and cashews. Serve immediately over white rice, if desired.
Although ingredients vary by brand, hoisin sauce is generally made with soybeans, chiles, and spices. This thick, dark-brown sauce is used both at the table and as a seasoning in cooking.