Add the chopped bacon to a 12-inch skillet over medium-high heat. Cook, stirring often until the bacon is beginning to render its fat, about 5 minutes. Add the kimchi, garlic, and the white parts of the green onions and cook for 2-3 mintues. Add the cooked rice, the soy sauce, and the fish sauce, and the reserved kimchi brine and mix well. Continue to cook, stirring often until the rice is heated through and the kimchi is evenly dispersed throughout the rice.
While the rice continues to cook, begin heating 1 Tablespoon of butter or neutral-flavored coking oil in a 10-inch skillet over medium-high heat. Crack the eggs into the skillet, add about 1 teaspoon to 1 Tablespoon of water and cover. Cook until the whites are set, but yolks are still runny (about 2-3 minutes), or cook the eggs to your desired doneness.
Once the rice is heated through, divide the rice into 4 bowls, serving 1 egg on top of each bowl. Garnish with the green parts of the green onions, and sesame seeds, if desired.
Notes
Bacon is optional. If you follow a vegetarian or plant-based diet, feel free to skip it. If you don't eat pork, feel free to use turkey bacon instead. If you opt to skip the bacon, add about 1 Tablespoon of neutral-flavored cooking oil to the skillet before adding the kimchi, garlic, and green onions.