To prepare the ingredients, use kitchen shears to cut the kimchi into small pieces. Dice the onion, chop the scallions, and cube the ham.
To stir-fry the base, in a large pan over high heat, add 1 tablespoon of cooking oil or butter. Add the onion and ham and stir-fry for about 1 minute until fragrant. Add the chopped kimchi and stir-fry for another minute.
To add the rice and seasonings, add the overnight rice and toss to combine evenly. Stir in the kimchi juice, gochujang, and a pinch of salt and stir-fry for about 1 minute until well combined. Add the scallions and give everything a quick toss.
To create crispy bits, in a small cast iron skillet over medium-high heat, add the sesame oil and press the kimchi fried rice into the pan. Cook undisturbed for 1–2 minutes until lightly crisped on the bottom.
To fry the egg, in a separate pan over medium heat, add 1 tablespoon of cooking oil or butter. Crack in the egg and season with a pinch of salt. Cook sunny-side up or to your preferred doneness.
To serve, top the kimchi fried rice with the fried egg and garnish with sesame seeds and roasted seaweed flakes.