Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the minced garlic and diced carrot, sautéing for 2-3 minutes until fragrant and the carrot is slightly tender.
Stir in the chopped kimchi and continue to cook for another 2-3 minutes, allowing the kimchi to caramelize slightly.
Add the cooked rice, breaking apart any clumps, and stir-fry everything together for about 4-5 minutes, ensuring the rice is evenly coated and heated through.
Push the fried rice to one side of the skillet. Pour the eggs into the cleared side and scramble them until fully cooked, then mix them into the rice.
Add the peas and green onions, along with the soy sauce and sesame oil. Stir everything together for another minute or so.
Season with salt and pepper to taste, adjusting as necessary.
Remove from heat, sprinkle with sesame seeds for garnish, and serve hot.