Heat a large non-stick skillet over medium-high heat until very hot.
Add the ground pork, sea salt, and black pepper to the skillet, breaking the meat into small crumbles with a spatula until browned and cooked through.
Stir in the minced garlic and grated ginger, sautéing for 60 seconds until the aromatics are fragrant.
Add the chopped kimchi and gochujang to the pork, stirring constantly for 2 minutes to allow the flavors to meld.
Push the pork and kimchi mixture to the outer edges of the pan and drizzle the sesame oil into the center.
Add the cooked rice into the oil, pressing it down firmly with the back of a spoon; let it sit undisturbed for 3 minutes to develop a golden, crispy crust.
Stir everything together, incorporating the tamari and half of the sliced green onions.
In a separate small non-stick pan, fry the egg to your preference, ideally leaving the yolk runny.
Transfer the fried rice to a bowl and top with the fried egg and the remaining fresh green onions.