Heat the vegetable oil in a large skillet or wok over medium heat.
Add the diced onion and sauté for about 2-3 minutes until softened.
Stir in the minced garlic and diced carrots, cooking for another 2 minutes or until the carrots are tender.
Add the chopped kimchi to the skillet, cooking for an additional 2-3 minutes to allow the flavors to meld.
Push the kimchi mixture to the side of the skillet and add the cooked jasmine rice into the cleared space.
Drizzle the soy sauce and gochujang over the rice. Stir everything together until well combined and heated through.
Add the frozen peas and sliced green onions, cooking for another 2 minutes.
If using eggs, push the fried rice to one side of the skillet and crack the eggs into the space. Stir and scramble until cooked, then mix into the rice.
Drizzle with sesame oil and season with salt and pepper to taste.