Heat 1 tbsp of the oil in a large frying pan, and add the garlic, ginger, broccoli and half the spring onions. Fry for 5-7 mins until softened, then add the kimchi and fry for a couple of mins more. Tip in the rice, breaking it up with the back of your spoon, then stir through the carrot. Cook for a min until all heated through, then push everything to the side of the pan.
Pour the remaining oil into the empty part of the pan, crack in the eggs, fry to your liking and season. Squeeze the lime juice over the rice and eggs, then scoop the rice into bowls. Top with the egg, coriander leaves, remaining spring onions and hot sauce, if using. Serve with lime wedges.