Rice: You will need day-old, cooked white rice (freshly made rice has too much moisture and will stick to the pan). Start by spreading freshly cooked rice on a tray to let it cool and dry out, 15 minutes. Divide cooked, cooled, and dried rice into 1-cup portions; store individually in zip-top plastic bags and freeze until ready to use. When you're ready to cook, place 2 cups frozen rice in a bowl; put on rubber gloves, and pour 1 tablespoon oil onto your gloved hands. Then crumble the rice in the bowl so the kernels separate and absorb the oil. Set aside.
Ingredient prep: Dice Chinese chives; place in a bowl and set aside. Peel and trim onion, then finely dice so the pieces are the size of a rice kernel; place in a bowl and set aside. Dice beef into small cubes; place in a bowl and set aside. Place kimchi on a flat surface. Cut away and discard the core and separate the layers; then spread out the kimchi and dice. (Kimchi dice should be larger than other ingredients.) Place in a bowl and set aside.
Fried rice: Preheat a wok over high heat until it starts to smoke, 7–10 minutes. While the wok is heating, preheat a small cast-iron skillet to cook the eggs, 1-2 minutes. When the skillet is smoking, add ½ tablespoon oil. Crack egg into skillet, season with a pinch of salt, and take skillet off the heat to finish cooking, 2 minutes. (Optional: If you want an egg for each serving, repeat with second egg and more oil.)
When the wok is smoking, add 1 tablespoon oil and the beef. Season with a pinch of salt. Do not toss or stir, so the beef can sear on one side, 30 seconds. Add 1 cup of the onions and 1 cup of the kimchi; toss for 30 seconds. Push the mixture to one side of the wok and add the rice, flattening it gently against the bottom of the wok; season the rice with salt, and allow to rest, 30 seconds. Flip kimchi mixture on top of the rice and let the rice cook for 1 minute; then add about half of the chives. After about 30 seconds, a light crust will form on the bottom of the rice (similar to socarrat in paella); when it does, vigorously toss and mix the fried rice, moving the wok around and breaking up rice clumps with your spatula, 30 seconds.
Move the fried rice to one side and tilt the wok; add the soy sauce by letting it trickle down the side of the wok and pool at the bottom. Allow it to reduce by ⅔; then mix everything together until thoroughly combined. Add sesame oil, most of the sesame seeds, and half the scallions; toss and mix until combined.
Remove wok from heat and transfer fried rice to a serving bowl. Top with fried egg, garnish with additional scallions and sesame seeds, and serve immediately.