Whisk the eggs with a pinch of salt in a small bowl. Heat 1 tablespoon of the oil in a large nonstick skillet over medium-high heat. Add the eggs and cook, without stirring, until almost set, about 1 minute. Flip the egg pancake with a rubber spatula and cook until just set on the other side, about 1 minute. Transfer to a cutting board and cut into thin strips.
Heat the remaining 1 tablespoon oil in the same skillet over high heat. Add the chicken and cook, stirring, until almost cooked through, about 2 minutes. Add the peas and carrots, peppers and scallions and continue to cook, stirring, until crisp-tender, about 2 minutes. Add the ginger and cook, stirring, 1 minute. Add the rice and Japanese Style Teriyaki Cooking Sauce and cook, stirring, until warmed through. Stir in the egg strips and divide among 4 bowls.
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