Heat ½ teaspoon of neutral oil in a large skillet over medium heat. Pour in the beaten eggs and gently stir to scramble, cooking for about a minute. Remove the eggs and set them aside.
Clean the skillet lightly and return it to the stove at medium heat. Add 1 tablespoon of oil, then toss in the chopped onion, diced carrots, and peas. Cook these, stirring regularly, until they soften, about 3 to 5 minutes.
Pour in the final tablespoon of oil along with the garlic, ginger, and the white and light green parts of the scallions. Stir briefly to combine. Add the chilled rice, soy sauce, and 1 tablespoon of sesame oil next. Mix everything to evenly coat the rice, then spread it flat in the pan. Let it cook mostly undisturbed for 3 to 5 minutes so the bottom can get a bit crispy and browned.
Finish by mixing in the remaining ½ tablespoon sesame oil, rice vinegar, and the cooked scrambled eggs. Taste and adjust seasoning if necessary. Garnish with the reserved dark green scallion tops, then serve hot.