Step 1

Beat eggs and ¼ teaspoon salt in bowl until well combined. Heat 2 teaspoons oil in 14-inch flat-bottomed wok or 12-inch carbon-steel or cast-iron skillet over medium-high heat until oil is just smoking. Add eggs and cook, stirring frequently, until very little liquid egg remains, 30 to 60 seconds. Transfer to large plate.

Step 2

Add 1 teaspoon oil to now-empty wok and reduce heat to medium. Add carrot and ¼ teaspoon salt and cook, stirring frequently, until just beginning to brown, 2 to 4 minutes. Add ham and cook, stirring frequently, until ham is warmed through, 1 to 2 minutes. Transfer to plate with eggs.

Step 3

Add scallion whites and remaining 1 tablespoon oil to now-empty wok. Cook, stirring constantly, until fragrant, about 1 minute. Add rice and stir until combined. (It's OK if some clumps of rice remain.) Spread into even layer. Sprinkle pepper and remaining 1 teaspoon salt evenly over rice. Continue to cook, stirring frequently and pressing on rice with spatula to break up clumps, until grains are separate and heated through, 2 to 5 minutes longer. Add peas, egg mixture, and scallion greens and cook, stirring frequently and using edge of spatula to break eggs into small pieces, until peas are warmed through, about 2 minutes. Serve.