Line a plate with paper towels. Place the bacon in a large skillet and cook over medium heat, turning a few times, until the bacon is crispy. Use tongs to transfer the bacon to the paper towels, and leave 1 tablespoon of the bacon fat in the skillet.
Return the pan to medium high heat and the kimchi. Stir for about 4 minutes, until the kimchi is nicely coated with bacon fat and hot throughout. Add the cooled rice, and stir occasionally for about 5 more minutes, until the rice is hot. Add half of the scallions, red pepper, soy sauce, and sesame oil. Stir until everything is well blended and hot, another 2 to 3 minutes. Crumble the bacon and stir it in at the end.
While the rice finishes cooking, in another large skillet, melt the butter over medium high heat. Crack the eggs into the pan and cook until the whites are set, but the yolks are still runny.
Divide the fried rice into 4 shallow bowls, and place a fried egg on top of each portion. Season with salt and pepper. Garnish the rest of the scallions, and the nori and sesame seeds if desired and serve hot.