01 - Heat 2 tablespoons of neutral oil in a large skillet or wok over medium-high heat. Add the sliced white parts of the scallions and fry for 2 to 3 minutes, stirring occasionally, until golden and crispy. Transfer to a plate lined with paper towels and set aside for garnish.
02 - In the same skillet, add the remaining 1 tablespoon of neutral oil. Add the minced garlic and diced carrot, then sauté for about 1 minute until fragrant and the carrot begins to soften.
03 - Add the chopped kimchi to the pan and cook for 2 to 3 minutes, allowing it to lightly caramelize. Pour in the reserved kimchi juice along with the gochujang, soy sauce, sugar, and black pepper. Stir everything together until well combined.
04 - Add the cold, day-old rice to the skillet, breaking up any clumps with a spatula. Stir-fry for 3 to 4 minutes, tossing frequently, until every grain is evenly coated with the sauce and heated through. Add the frozen peas and continue cooking until warmed.
05 - Drizzle the toasted sesame oil over the rice and stir to incorporate. Fold in the sliced green parts of the scallions, reserving a handful for garnish. Taste and adjust the seasoning with additional soy sauce or gochujang as desired.
06 - If using, heat a small nonstick pan over medium heat with a light coating of oil. Fry the eggs sunny-side up until the whites are set but the yolks remain runny, about 2 to 3 minutes.
07 - Divide the fried rice between two bowls. Top each portion with the crispy scallion whites, reserved fresh scallion greens, and a fried egg if desired. Serve immediately while hot.