To make day old rice – place 1 cup jasmine rice and 1 1/2 cups of water in a small sauce pan. Bring to a boil. Stir well. Reduce the heat to low, cover the pan and let the rice simmer for 10 minutes or until all the water is absorbed and the riced is cooked through. The rice must be fluffy and separate, not mushy. Spread the rice out on a platter or large plate. Let it cook completely. Then cover refrigerate it over night.
Heat the oil on high heat in a wok. Add the onion, green pepper if using, crushed pepper if using, and garlic. Sauté until fragrant, about 1 minute.
Add the sliced kimchi and cook for 1 minute. Then add the rice and soy sauce. Stir on high heat until everything is well combined and some of the rice is lightly brown. Taste the fried rice for salt. Sprinkle chopped scallions on top.
Heat a small skillet with a few drops of oil on medium heat. Carefully break open an egg onto the skillet. Let it cook undisturbed, until the white is set, but the yellow is still a little runny. Carefully slide the egg on top of the rice. Repeat with the other egg.