First, warm 1 tablespoon of vegetable oil in a large skillet or wok over medium high heat. Pour in the beaten eggs, scramble them quickly until they are cooked through, and then set them aside on a plate.

Next, heat the remaining 1 tablespoon of vegetable oil and 1 tablespoon of sesame oil in the same skillet. Add the diced onion and minced garlic, and saut for about two minutes. Stir in the thawed peas and carrots, and cook for another two minutes until they are warm.

Now, add the cold cooked rice to the skillet. Use a spatula to break up any clumps, and fry for three to four minutes. Drizzle the soy sauce and the remaining 1 tablespoon of sesame oil over the rice. Toss everything continuously until the rice is evenly coated.

Finally, gently fold in the scrambled eggs and the sliced green onions. Toss for one more minute, and serve your delicious fried rice hot.