To prepare the sauce and eggs: In a small bowl, mix together the white pepper, soy sauce, and oyster sauce. In a separate bowl, beat the eggs and set aside.
To stir-fry the vegetables: Heat a wok over high heat and 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: Add the overnight rice and stir-fry over high heat for about 1 minute, breaking up any clumps as you toss.
To combine and serve: Return the vegetables to the wok and pour in the sauce. Stir-fry until everything is evenly combined and heated through. Add the scallions, give everything one final toss, and serve immediately.