Heat vegetable oil in a medium pot over medium heat.
Add chopped kimchi and cook for 3-4 minutes, stirring occasionally, until slightly softened.
Add uncooked rice to the pot and stir to combine with the kimchi.
Pour in water, kimchi juice, gochujang, soy sauce, and sugar. Stir well to mix all ingredients.
If using cooked pork belly or bacon, add it to the pot and stir to combine.
Bring the mixture to a boil, then reduce heat to low and cover the pot with a tight-fitting lid.
Simmer for 15-18 minutes, or until the rice is cooked and liquid is absorbed.
While the rice cooks, heat a small non-stick pan over medium heat and fry the egg sunny side up.
Remove the pot from heat and let it sit covered for 5 minutes.
Fluff the kimchi rice with a fork and transfer to serving bowls.
Top each bowl with the fried egg, sliced green onions, and sprinkle with toasted sesame seeds.
Serve immediately.