Preheat a wok or cast-iron skillet over high heat. Add 2 tbsp. oil, swirl to coat the pan and add the eggs. Cook, stirring constantly, until the eggs are scrambled, 1 minute. Transfer the eggs to a plate. Wipe the pan clean and return to the heat.
Add the remaining 1/4 cup oil; swirl to coat. Add the chicken, scallion whites and ginger. Cook, stirring frequently, until the chicken is golden, about 2 minutes. Stir in the rice and press into the pan. Cook, stirring and pressing, until the rice is sizzling, about 2 minutes.
Return the eggs to the pan; add the peas, 2 tbsp. soy sauce, the vinegar and sesame oil. Cook, stirring, until heated through, about 1 minute. Serve with more soy sauce and the scallion greens.