2 tablespoons kochujang (Korean chili-soy-bean paste) or other Asian chili
4 large eggs
Toasted sesame seeds and torn sheets of nori, for serving
In a large saucepan, cover the rice with the water, add a pinch of salt and bring to a boil. Cover and cook over very low heat until the rice is tender and the water is absorbed, about 18 minutes. Remove from the heat and let stand, covered, for 5 minutes.
Meanwhile, in a large skillet, heat 1 tablespoon of the vegetable oil. Add the scallions, carrot and ham and stir-fry over high heat until the vegetables are softened, about 4 minutes. Stir in the kimchi and cook for 1 minute.
Transfer the vegetables and ham to a large bowl. Stir in the rice, kimchi and chili paste. Cover and keep warm.
Heat the remaining 2 tablespoons of vegetable oil in the skillet. Crack the eggs into the skillet and cook over moderately high heat until the edges are just set, about 2 minutes. Flip the eggs and cook until the whites are set and the yolks are still runny, about 1 minute. Spoon the rice mixture into bowls and top with the eggs. Garnish with the sesame seeds and nori and serve.