Break cold rice into loose grains with clean fingers or a fork. Beat eggs until fully blended. Dice carrot and onion into quarter-inch pieces, thaw and pat peas dry, and measure all oils, sauce, and aromatics before heating the pan.
Heat 1 teaspoon oil in a 12-inch skillet over medium heat. Cook beaten eggs for 1 to 2 minutes, stirring, until just fully set. Transfer to a heatproof bowl.
Add 2 teaspoons oil to the skillet over medium-high heat. Cook onion and carrot for 3 to 4 minutes until the carrot loses its raw crunch. Add peas, scallion whites, garlic, and ginger and cook for 30 to 60 seconds. Transfer everything to the bowl with the eggs.
Add 1 tablespoon oil and 2 cups rice to the skillet over medium-high heat. Spread across the pan and cook for 3 to 4 minutes, lifting and turning every 30 to 45 seconds until the grains are separate and hot.
Add 1 tablespoon soy sauce, half the white pepper, and half the egg-vegetable mixture. Toss for 1 to 2 minutes until the rice reaches 165°F throughout. Turn off the heat, fold in 1/2 teaspoon sesame oil and half the scallion greens, and transfer to a serving platter.
Return the skillet to medium-high heat and repeat steps 4 and 5 with the remaining rice, oil, soy sauce, pepper, egg-vegetable mixture, sesame oil, and scallion greens. Serve promptly.
