Make sure your leftover rice is chilled, as it helps prevent the rice from sticking together.Finely dice the carrots and mince the garlic.Beat the eggs in a bowl and season with a pinch of salt and pepper.Slice the scallions, separating the white and green parts. Heat 2 tablespoons of vegetable oil in a large wok or pan over medium-high heat.Add the minced garlic and sauté for about 30 seconds until fragrant.Add the diced carrots and stir-fry for 2-3 minutes until they start to soften. Add the chilled leftover rice to the wok. Break up any clumps and stir-fry for a few minutes until the rice is heated through and well combined with the vegetables. Push the rice mixture to the sides of the wok, creating a well in the center.
Pour the beaten eggs into the well and let them sit for a moment until they begin to set.Scramble the eggs with a spatula and mix them into the rice and vegetables. Add oyster sauce, soy sauce, and sesame oil to the mixture. Stir well to evenly coat the rice with the sauces.
Add the sliced green parts of the scallions and stir-fry for an additional 1-2 minutes.
Taste the fried rice and adjust the seasoning with salt and pepper if needed.
Transfer the egg-fried rice to a serving dish, garnish with the remaining white parts of the scallions, and serve hot.