Heat oil in large frying pan over high heat. Stir in minced beef and white parts of spring onion then reduce heat to medium. Cook and stir mince and onion until meat is browned and onion is fragrant, 1 to 2 minutes.
Stir kimchi and gochujang into meat mixture and cook until warmed through and fragrant, 2 to 4 minutes. Add rice then cook and stir until rice is heated through, 3 to 5 minutes more.
Drizzle sesame oil over rice mixture and stir to coat. Garnish with green parts of spring onion.
Melt 1 teaspoon butter in a frying pan over medium-high heat. Crack egg into the pan and cook until white is completely set and yolk is still runny, 3 to 4 minutes. Place egg over fried rice.