Instructions

Whisk ⅓ cup ketchup, 2 tablespoons soy sauce, 2 teaspoons rice vinegar, and ½ teaspoon pepper together in small bowl; set aside.
Beat 3 eggs with ¼ teaspoon kosher salt in medium bowl. Heat 2 teaspoons vegetable oil in 14-inch flat-bottomed wok or 12-inch cast-iron skillet over medium-high heat until just smoking. Add eggs and cook, stirring constantly, until soft curds form and very little liquid egg remains, about 30 seconds. Transfer to large plate.
Heat 1 teaspoon oil in now-empty wok over medium-high heat until shimmering. Add 1 carrot, peeled and cut into ¼-inch dice, and remaining ¼ teaspoon salt and cook, stirring frequently, until lightly browned and crisp-tender, about 2 minutes. Add 2 cups shredded cabbage and cook, stirring frequently, until tender and bright green, about 2 minutes. Stir in ½ cup frozen peas and cook until thawed, about 1 minute. Transfer vegetable mixture to plate with eggs.
Heat remaining 1 tablespoon oil in now-empty wok over medium-high heat until shimmering. Add thinly sliced whites of 4 scallions and 4 minced garlic cloves and cook until fragrant, about 1 minute. Add 4 cups cooked and cooled basmati rice and stir to combine. Spread into even layer and cook, stirring occasionally and pressing down with spatula to break up clumps, until grains are separated and heated through, 2 to 3 minutes.
Drizzle sauce evenly over rice. Cook, stirring constantly, until sauce coats every grain and begins to caramelize lightly on bottom of wok, about 2 minutes. Return egg and vegetable mixture to wok. Add thinly sliced greens of 4 scallions and cook, stirring frequently and breaking eggs into bite-size pieces, until heated through, about 1 minute. Serve.