Break up the cold day-old rice to separate the grains, then cut chicken into ¾-inch pieces and toss with 1 tablespoon soy sauce and a pinch of white pepper. In a small bowl, mix the remaining 2 tablespoons soy sauce, oyster sauce, fish sauce, and 1 tablespoon sesame oil to make the sauce; set aside.
Crack the eggs into a small bowl, add a pinch of salt, and beat lightly with a fork until combined. Set aside.
Mince the garlic, grate the ginger, and slice the green onions, keeping the white parts and green parts in separate piles. Thaw and drain the peas and carrots thoroughly.
Heat the wok over high heat until lightly smoking, add 1 tablespoon neutral oil, then cook the seasoned chicken in a single layer for 1–2 minutes per side until golden and cooked through. Transfer to a bowl and set aside.
Return the wok to medium-high heat, pour in the beaten eggs, and scramble quickly for 30–45 seconds until just set but still slightly glossy. Push to the side or remove to the chicken bowl.
Add the remaining tablespoon of neutral oil, then stir-fry the garlic, ginger, and white parts of the green onions for about 45 seconds until fragrant. Add the peas and carrots and stir-fry for 1–2 minutes.
Add the cold rice to the wok over high heat, spread it into an even layer, and let it sit undisturbed for 45–60 seconds to toast. Toss, press again, and repeat 3–4 times over about 3–4 minutes until the rice looks dry, glossy, and lightly golden.
Return the chicken and eggs to the wok, pour the prepared sauce evenly over everything, and toss vigorously for 1–2 minutes until the sauce is fully absorbed and everything is well combined. Taste and adjust seasoning.
Remove from heat, drizzle the remaining 1 tablespoon of toasted sesame oil over the rice, toss once more, and garnish with the green parts of the sliced green onions. Serve immediately.