Whisk together the soy sauce, oyster sauce, rice vinegar, sesame oil, cornstarch, chicken broth, and sugar in a small bowl until the cornstarch dissolves completely.

Slice the chicken breast into bite-sized three-quarter inch cubes and cut all vegetables into uniform sizes for even cooking.

Place a wok or large skillet over high heat and let it heat until smoking hot, about 1 to 2 minutes.

Add 1 tablespoon of vegetable oil to the hot pan and arrange the chicken in a single layer; cook without stirring for 2 to 3 minutes until the bottom is golden, then stir and cook another 2 to 3 minutes until cooked through. Transfer the chicken to a plate.

Add the remaining tablespoon of oil, then add the carrots and snap peas; stir constantly for 2 minutes until they begin to soften but remain crisp.

Add the bell pepper, mushrooms, garlic, and ginger; stir continuously for 1 to 2 minutes until fragrant and vegetables are tender-crisp.

Pour the sauce into the pan and return the chicken; stir constantly for 1 to 2 minutes until the sauce thickens and evenly coats the ingredients, then taste and adjust seasoning with salt and pepper if needed.

Transfer the chicken chop suey to a serving platter or individual bowls and serve immediately over steamed rice or crispy noodles.