Preheat the oven to 350 degrees Fahrenheit.

Put the cashews in a single layer on a baking sheet. Toast in the oven for 5 minutes, or until fragrant. Put aside to crisp up as they cool.

Meanwhile, make the sauce by whisking together the water, cornstarch, hoisin sauce, and soy sauce in a small bowl. Set aside.

In a large mixing basin, combine the chicken pieces. Toss with the salt and pepper until evenly coated.

Heat 1 tablespoon of the vegetable oil in a large nonstick skillet over high heat until extremely hot. Stir-fry half of the chicken in the skillet for 3 minutes, or until lightly browned but not cooked through. Place on a platter.

Add the remaining chicken, garlic, and white sections of the scallions to the skillet, followed by the remaining tablespoon vegetable oil. Stir-fry for 3 minutes, or until the chicken is lightly browned but not cooked through. Put the first batch of chicken back in the pan. Reduce the heat to medium and add the rice vinegar; simmer for 30 seconds, or until it has evaporated.

Cook, tossing constantly, until the chicken is cooked through and the sauce is properly thickened, about 1 minute. Take the pan off the heat. Combine the scallion greens, cashews, and sesame oil in a mixing bowl. Serve right away.