In a large re-sealable bag, toss chicken with cornstarch and pepper until chicken is coated.
In a large skillet or wok, heat 1 ½ tablespoons oil over medium-high heat. Cook half the chicken, turning often, until golden brown and cooked through. Transfer to a plate.
Add remaining oil and chicken to skillet along with the garlic. Cook, turning often, until second batch of chicken is browned and cooked through. Return first batch of chicken to pan. Add scallions and bok choy. Stir-fry until crip-tender. Add vinegar; cook until evaporated, about 30 seconds, scraping up brown bits on bottom of pan.
Add cashews, hoisin sauce and 1/4 cup water; cook, tossing, until cashews are warmed through, and sauce is at a good consistency for your family. Serve immediately over rice, topped with a few cashews and thinly sliced pieces of scallion, if desired.