In a wok or large nonstick skillet, heat 1 tablespoon oil over high. Meanwhile, in a small bowl, lightly beat eggs with 1/4 teaspoon soy sauce to combine. Add eggs to wok and swirl to coat bottom of pan. Cook, without stirring, until almost set, 1 minute, then fold in thirds with a spatula. Transfer cooked eggs to a work surface and cut into 1/2-inch pieces.
Add 1 tablespoon oil to wok and swirl to coat. Add garlic, ginger, and scallion whites and cook, stirring constantly, until fragrant, 30 seconds. Add pork and cook, breaking up meat with a wooden spoon, until just cooked through, about 3 minutes. Add carrots, peas, and rice and stir to combine. Add cooked egg, 2 tablespoons soy sauce, and vinegar and cook, stirring constantly, until rice is coated, about 1 minute. Let cook, undisturbed, until warm, about 1 minute. Top with scallion greens and serve.
Leftover cooked rice is perfect in this dish because it won't stick together in the skillet. For a lighter version, substitute ground turkey for the pork.