01 - Heat vegetable oil and butter in a large nonstick skillet or wok over medium-high heat until melted and shimmering.
02 - Add the white parts of the scallions and minced garlic. Sauté for 1-2 minutes until fragrant and just starting to soften, being careful not to burn the garlic.
03 - Add the chopped kimchi and cook for 2-3 minutes, stirring often, until kimchi is heated through and slightly caramelized at the edges.
04 - If using eggs, push the kimchi mixture to one side. Crack the eggs into the empty side of the pan and scramble until just set, then mix into the kimchi.
05 - Add the rice, breaking up any clumps with a spatula. Stir-fry for 2-3 minutes, allowing some grains to get slightly crispy and golden.
06 - Pour in the soy sauce, kimchi juice, gochujang (if using), and black pepper. Mix thoroughly to distribute the flavor evenly throughout the rice.
07 - Drizzle with toasted sesame oil and toss to combine, ensuring the aroma is well distributed.
08 - Remove from heat. Stir in the green parts of the scallions, allowing them to wilt slightly in the residual heat.
09 - Serve hot, topped generously with crispy fried shallots and toasted sesame seeds for crunch and texture.