Heat a large skillet over medium-high heat and add the diced pork shoulder, seasoning with the sea salt and black pepper.
Sear the pork until the fat renders and the edges become golden and crispy, about 5-7 minutes.
Add the minced garlic, grated ginger, and chopped kimchi to the pan, sautéing for 2 minutes until fragrant.
Stir in the chilled jasmine rice and gochugaru, pressing the rice down with a spatula to develop a toasted crust on the bottom.
Push the rice mixture to one side of the pan and pour in the egg whites, scrambling them until just set before mixing into the rice.
Drizzle with coconut aminos and toasted sesame oil, tossing everything together to combine all the flavors.
In a separate small non-stick pan, fry the large egg until the whites are set but the yolk remains beautifully runny.
Serve the fried rice in a bowl topped with the fried egg and a generous sprinkle of sliced green onions.