In a small bowl, whisk together 1/4 cup water, 2 teaspoons cornstarch, 1/4 cup hoisin sauce, and 1 tablespoon soy sauce until smooth. Set the sauce aside.
Place the 3/4 cup roasted, unsalted cashews in a small bowl and set aside (no toasting needed since they are already roasted).
Put the 1 1/2 pounds chicken pieces in a large bowl. Sprinkle with 1/2 teaspoon salt and 1/4 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. Add half of the chicken in a single layer and stir-fry until the pieces are 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 minced garlic cloves, and the white parts of the 8 scallions. Stir-fry until this batch is lightly browned but not cooked through, about 3 minutes.
Return the first batch of chicken to the skillet. Reduce the heat to medium, add 2 tablespoons rice vinegar, and cook, stirring, until the vinegar has mostly evaporated, about 30 seconds.
Stir the reserved sauce again (to re-incorporate any settled cornstarch) and pour it into the skillet. Cook, tossing or stirring, until the chicken is cooked through and the sauce has thickened, about 1 minute.
Remove the skillet from the heat. Stir in the green parts of the scallions, the reserved cashews, and 1/4 teaspoon sesame oil. Serve immediately.