To prepare the sauce and eggs, in a small bowl, whisk together the white pepper, soy sauce, and oyster sauce. In a separate bowl, beat the eggs and set aside.
To stir-fry the vegetables, in a wok over high heat, add 1 tablespoon of cooking oil. Add the onion, peas, carrots, and corn and stir-fry for about 30 seconds until slightly softened and fragrant. Remove and set aside.
To scramble the eggs, in the same wok over high heat, add the remaining 1 tablespoon of cooking oil. Pour in the beaten eggs and stir-fry until partially cooked.
To stir-fry the rice and combine, add the overnight rice to the wok and stir-fry over high heat for about 1 minute, breaking up any clumps so the grains separate. Return the vegetables to the wok and pour in the sauce. Stir-fry until everything is evenly combined and heated through. Lastly, add the scallions and give everything one final toss before serving immediately.