Heat a large cast-iron skillet over medium-high heat until very hot.
Add the ground pork, sea salt, and black pepper to the skillet, cooking until browned and crispy while breaking it into small crumbles.
Push the pork to one side of the pan and add the sesame oil, minced garlic, and grated ginger to the empty space, sautéing for 30 seconds until fragrant.
Stir in the chopped kimchi and gochujang, mixing with the pork and aromatics for 2 minutes to caramelize the kimchi juices.
Add the cooked rice to the pan, pressing it down firmly with a spatula to create an even layer; let it cook undisturbed for 3-4 minutes to develop a crispy crust.
Drizzle the tamari over the rice, toss everything together to combine, and remove the skillet from the heat.
In a separate small non-stick pan, fry the egg over medium heat until the whites are set and lacy but the yolk remains runny.
Transfer the fried rice to a bowl and top with the fried egg and sliced green onions before serving.