Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add the lean ground beef to the skillet and cook, breaking it apart with a spatula, until browned and cooked through, about 5-6 minutes. Drain excess fat if necessary.
Add the chopped onion and minced garlic to the beef. Cook for 2-3 minutes until the onion is translucent and fragrant.
Stir in the shredded carrots and thawed peas. Cook for another 2 minutes until the vegetables are slightly tender.
Push the beef and vegetable mixture to one side of the skillet. Add the remaining 1 tablespoon of vegetable oil to the empty side of the skillet.
Crack the eggs into the oil and scramble them until just set, about 1-2 minutes.
Mix the scrambled eggs into the beef and vegetables.
Add the chilled cooked rice to the skillet. Stir well to combine all ingredients evenly.
In a small bowl, whisk together the gochujang, soy sauce, sesame oil, and black pepper.
Pour the sauce over the rice mixture and stir thoroughly to coat all the rice and beef evenly.
Cook for an additional 3-4 minutes, stirring frequently, until the rice is heated through and slightly crispy on the bottom.
Remove from heat and stir in the sliced green onions.
Transfer to serving plates and garnish with toasted sesame seeds before serving.