Place the cashews on a baking sheet in a single layer. Roast in the oven at 180 degrees for about 5 minutes. Set aside
Meanwhile, prepare the sauce: in a small bowl, whisk together the water, cornstarch, hoisin sauce, and soy sauce. Set aside.
Place the chicken pieces in a large bowl. Sprinkle with salt and pepper and mix to coat evenly.
In a large skillet, heat 1 tablespoon of oil over high heat until very hot. Add half of the chicken to the pan and stir-fry until lightly golden but not completely cooked, about 3 minutes. Transfer to a plate.
Add the remaining tablespoon of oil to the pan; then add the remaining chicken, garlic, and white parts of the green onions. Stir-fry until the chicken is lightly golden but not completely cooked, about 3 minutes. Return the first batch of chicken to the pan. Lower the heat to medium and add the rice vinegar; cook until evaporated, about 30 seconds.
Add the sauce mixture to the chicken; cook, stirring, until the chicken is fully cooked and the sauce is well thickened, about 1 minute. Remove from heat. Stir in the green parts of the green onions, cashews, and sesame oil. Serve immediately. (Personally, I love it with sushi rice)