In a small bowl, whisk together the soy sauces, oyster sauce and sesame oil and set aside.
Heat 1 tablespoon of vegetable oil in a large wok or skillet over high heat. When you see wisps of smoke, add the chicken and stir-fry until it is cooked through and no longer pink. Remove the chicken from the wok and set it aside.
Add another tablespoon of vegetable oil to the wok. Add the peas, carrots, mushrooms, green onions, and garlic and stir-fry for 2-3 minutes until the vegetables are tender.
Push the vegetables to one side of the wok and add the beaten eggs to the other side. Scramble the eggs until they are cooked through, then mix them with the vegetables.
Add the cooked rice and cooked chicken to the wok and stir-fry everything together for 2-3 minutes.
Pour the sauce over the rice and chicken and stir-fry for another 2-3 minutes until everything is well coated and heated through.
Serve the chicken fried rice hot, garnished with additional green onions if desired.