In a small bowl, whisk together the gochujang, kimchi juice, and mirin or sugar. Set aside. In a large wok, cast-iron, or other nonstick skillet, cook the bacon (if using) over medium heat until almost crisp and the fat has rendered, about 5 minutes. If not using bacon, in the wok or skillet, heat the oil or oil/butter mix.
To the bacon fat or oil/butter mix in the skillet, add the onion, garlic, ginger, and any other protein (if using) and cook, stirring frequently, until the onion has become a bit translucent, 2 to 3 minutes.
Stir in the vegetables, kimchi, and kimchi juice/ gochujang mixture and cook, stirring constantly, until the vegetables have softened and the sauce has evaporated a bit, about 5 minutes. Add the cold rice and break up clumps with a wooden spoon or spatula, tossing to coat. Add the soy sauce and sesame oil and toss to coat. Keep cooking, stirring, and tossing until thoroughly mixed and piping hot, 2 to 3 minutes.
Reduce the heat to low and let sit to brown a bit while you fry the eggs sunny-side up in butter or a neutral/sesame oil mix.
When the eggs are ready, scrape up the rice, hopefully with a few little browned bits, and fill a medium soup bowl with one-quarter of the rice. Place a plate on top of the bowl and then invert to produce a dome of rice. Garnish with a fried egg, a nori strip, and some green onions and sesame seeds. If you like it spicier, drizzle with a bit of the diluted gochujang. Repeat for the remaining portions of rice.