Warm ½ teaspoon of the oil in a large skillet over medium heat. Pour in the beaten eggs, stir continuously for about a minute until scrambled, then transfer to a bowl and set aside.
Clean the skillet and return it to medium heat. Add 1 tablespoon of oil and toss in the onion, carrots, and peas. Cook, stirring frequently, for 3 to 5 minutes until the vegetables soften.
Pour the remaining tablespoon of oil into the pan along with the garlic, fresh ginger, and the white plus light green sections of the scallions. Stir briefly before adding the chilled rice, soy sauce, and 1 tablespoon of sesame oil. Mix well to coat the rice, then press it flat against the pan’s surface. Let it cook, stirring occasionally, for 3 to 5 minutes to let the rice develop a lightly crisp texture.
Add the leftover ½ tablespoon sesame oil, rice vinegar, and the cooked scrambled eggs back into the skillet. Mix everything thoroughly. Adjust seasoning if needed. Top with the reserved scallion greens and serve hot.