Add 2 tablespoons of vegetable oil to a frying pan or wok and crank up the heat to high. Add the garlic and spring onions and when they have started to turn golden (after just a minute or two), add the carrot, cabbage and green pepper. Ensure that the heat remains high as you want the vegetables fry quickly and caramelise, rather than stew.
After 2 minutes, add the rice to the frying pan along with the peas, soy sauce and chopped kimchi. Splash about 3 tablespoons of warm water into the pan. The steam will soften the rice and bring all the ingredients together. Give everything a good toss to combine and within a minute or so your fried rice will be ready. Taste and season with salt if you feel the dish needs it (the kimchi and soy sauce are already salty, so be cautious).
Fry the eggs in a drizzle of vegetable oil in a non-stick pan over a medium heat until the edges are crispy but the yolks are still runny. Place the rice in 4 bowls and top each one with the fried eggs and a drizzle of chilli oil. Eat immediately, with some extra kimchi on the side.