Whisk the soy sauce, toasted sesame oil, sugar, and black pepper in a small bowl. Break up any clumps in the cold rice.
Heat 1 tablespoon neutral oil in a large skillet or wok over medium-high heat. Add the beaten eggs and scramble gently until just set; transfer to a plate.
Add the remaining oil. Cook the carrots and scallion whites for 2 minutes, then stir in the peas and garlic for 30 seconds.
Add the rice and spread it across the pan. Let it sit briefly, then toss and stir-fry for 3 to 4 minutes until hot.
Return the eggs and pour in the soy mixture. Toss until evenly coated, finish with scallion greens, and serve right away.