Heat a large nonstick skillet or wok over high heat and then swirl in 1 tablespoon of the oil. When the oil begins to smoke, add the egg and swirl the skillet to make a flat egg pancake that's only half set, about 10 seconds; scoop out onto a plate.
Add the chicken to the skillet, sprinkle with 1/4 teaspoon salt and cook, stirring constantly, until golden brown and just cooked through, about 4 minutes. Transfer to a bowl. Add the remaining tablespoon oil, then add the shiitakes and cook, stirring constantly, until golden, about 3 minutes. Add the ginger, Shaoxing wine, soy sauce and 1/4 teaspoon salt and stir until the ginger is tender, 1 to 2 minutes.
Add the rice, stirring to break up any clumps, and spread it out in the skillet. Cook until heated through, about 3 minutes. Return the egg, chicken and any juices to the skillet and cook, stirring and breaking up the egg, to mix it in thoroughly, about 1 minute. Season with additional salt if needed. Drizzle with the sesame oil, sprinkle with scallions and serve.
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