Prepare the sauce:
In a small bowl, whisk together the water, cornstarch, hoisin sauce, and soy sauce. Set aside.
In a large nonstick skillet, heat 1 tablespoon of the vegetable oil over high heat until very hot.
Add half of the chicken to the skillet and stir-fry until lightly browned but not cooked through, about 3 minutes.
Transfer to a plate.
Add the remaining tablespoon vegetable oil to the skillet; then add the remaining chicken, garlic and white parts of the scallions.
Stir-fry until the chicken is lightly browned but not cooked through, about 3 minutes.
Return the first batch of chicken to the pan. Turn the heat down to medium and add the rice vinegar; cook until evaporated, about 30 seconds.
Add the sauce mixture to the chicken; cook, tossing, until the chicken is cooked through and the sauce is nicely thickened, about 1 minute.
Remove from the heat. Stir in the scallion greens, cashews and sesame oil.