Start by combining all the sauce ingredients in a small bowl—soy sauce, oyster sauce, sugar, and cornstarch mixed with water. Stir well until the cornstarch is fully dissolved. This sauce will thicken later as it cooks, creating a glossy coating for the chicken and vegetables.
Next, season the chicken cubes with salt and black pepper. Lightly coat them with flour in a mixing bowl, ensuring each piece is evenly covered. The flour helps give the chicken a slight crust when pan-fried, which adds texture and helps the sauce cling better.
Set the sauce and chicken aside while you prepare the vegetables. Cube the red and green bell peppers, quarter the onion, mince the garlic, and chop the green onions—keeping the white and green parts separate for layered cooking later.
In a large skillet or wok, heat 1 tablespoon of vegetable oil over medium heat. Add the cashews and toast them until they are golden brown. Be sure to stir constantly, as they can burn quickly. Once golden, remove the cashews and set them aside.
Add the remaining vegetable oil and sesame oil to the same skillet. Turn the heat to medium-high and add the flour-coated chicken. Fry until the pieces are golden brown and fully cooked through, about 5–7 minutes. Remove the chicken from the skillet and set it aside on a plate.
In the same pan, add the red and green bell peppers along with the onion. Stir-fry for about 2–3 minutes until slightly softened but still crisp. Then add the white part of the green onions and minced garlic. Cook for another minute until fragrant.
Pour the sauce mixture into the skillet and stir constantly. Within a few minutes, the sauce will begin to bubble and thicken. Once it reaches a glossy consistency, return the cooked chicken to the pan.
Mix everything together well so the chicken and vegetables are fully coated in the sauce. Stir in the green part of the onions and toasted cashews. Give it one last stir and remove from heat.