If you don’t have leftover rice, steam two cups of rinsed rice (short grain preferably but jasmine rice also works) in a rice cooker. When the rice is done, scoop it out and loosely spread it over a large tray and set aside to cool.
In a round flat-bottomed wok, heat one tablespoon of butter over medium heat, add the crunchy white parts of the scallions or spring onions and stir-fry until they start to soften.
To the wok, add the diced onion and carrot and continue to stir-fry for a few minutes until the onion softens and sizzles and the scallions and onions begin to brown and even char a little. Transfer it all to a dish.
Use a paper kitchen towel to wipe out the wok, add a tablespoon of vegetable oil, heat over medium, then add the chopped kimchi, stir-fry for a couple of minutes until it starts to brown, then add the kimchi juice, gochujang and water.
Gradually add the rice, a couple of scoops at a time, and continue stir-frying to combine the ingredients together. Once all the rice is in and well-combined, add the sesame oil, stir in well, taste, and, if it needs it, add half a teaspoon of salt – or to your taste, try the rice again, and adjust seasoning to your palate.
Turn the heat off and set aside, and in a small pan, fry the eggs so the yolk is still soft and runny – or to your liking.
Distribute the fried rice between bowls, slide an egg on top of each, sprinkle with the finely sliced roasted seaweed, sesame seeds (or furikake), the finely sliced green scallions or spring onions, and, if you like your food spicy, sprinkle on some gochugaru or other chilli flakes.
Serve immediately and use chopsticks to mix in the runny yolk and garnishes. Enjoy!