Place the ¾ cup roasted, unsalted cashews in a small bowl and set aside.
In a small bowl, whisk together ¼ cup water, 2 teaspoons cornstarch, ¼ cup hoisin sauce, and 1 tablespoon soy sauce until smooth; set the sauce mixture aside.
Place the 1½ pounds chicken pieces in a large bowl. Sprinkle with ½ teaspoon salt and ¼ teaspoon freshly ground black pepper and toss to coat evenly.
Heat a large nonstick skillet over high heat until very hot. Add 1 tablespoon vegetable oil and swirl to coat the pan. Add half of the chicken and stir-fry until lightly browned but not cooked through, about 3 minutes. Transfer this first batch to a plate.
Add the remaining 1 tablespoon vegetable oil to the skillet. Add the remaining chicken, the 6 cloves garlic (minced), and the white parts of the 8 scallions (sliced into 1‑in/2.5‑cm pieces). Stir-fry until the chicken is lightly browned but not cooked through, about 3 minutes.
Return the first batch of chicken to the skillet. Reduce the heat to medium and add 2 tablespoons rice vinegar; cook, stirring, until the vinegar has mostly evaporated, about 30 seconds.
Stir the sauce mixture once more, then add it to the skillet. Cook, tossing or stirring, until the chicken is cooked through and the sauce has thickened and glazed the chicken, about 1 minute.
Remove the skillet from the heat. Stir in the green parts of the scallions, the reserved ¾ cup cashews, and ¼ teaspoon sesame oil.
Serve immediately.