Preheat the oven to 350°F (175°C). Spread the cashews on a baking sheet in a single layer and toast them in the oven until fragrant, about 5 minutes. Allow them to cool; they will crisp up as they cool.

In a small bowl, whisk together the water, cornstarch, hoisin sauce, and soy sauce until smooth. Set this mixture aside for later.

Place chicken pieces in a large bowl. Sprinkle with salt and black pepper, and toss to coat evenly.

In a large nonstick skillet, heat 1 tablespoon of vegetable oil over high heat until very hot. Add half of the seasoned chicken and stir-fry until lightly browned but not completely cooked, about 3 minutes. Transfer this batch to a plate.

In the same skillet, add the remaining tablespoon of vegetable oil along with the other half of the chicken, minced garlic, and the white parts of the scallions. Stir-fry until the chicken is browned but still not fully cooked, about 3 minutes.

Return the first batch of chicken to the skillet. Lower the heat to medium and add the rice vinegar, cooking until it evaporates, approximately 30 seconds.

Stir in your hoisin sauce mixture. Cook and toss until the chicken is cooked through and the sauce thickens, about 1 minute.

Remove the skillet from heat and stir in the scallion greens, toasted cashews, and sesame oil. Serve immediately.