Add onion and carrot; cook, stirring frequently, until just starting to brown (about 5 minutes).
Mix in garlic and ginger; cook, stirring constantly, until fragrant (about 30 seconds).
Add kimchi, kimchi juice, gochujang, and soy sauce to skillet. Mix well, then cook until liquid is reduced and thickened, stirring frequently (about 4 to 5 minutes).
Add rice to skillet. Cook until rice is coated with kimchi sauce and is heated through (no large clumps of rice should remain).
Drizzle sesame oil over rice and stir well.
Divide rice among 4 bowls. Top with a fried egg and sprinkle with green onions. Enjoy!
Notes
*Not all kimchi is vegetarian / vegan. Read the ingredients and/or look for packaging that's labeled as such.** Use tamari to make this recipe gluten-free.***Skip the eggs to make this recipe vegan friendly.