Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the diced chicken and cook until it's fully cooked through and lightly browned. Remove the chicken and set it aside.
In the same skillet, add the beaten eggs. Cook, stirring gently, until they are lightly scrambled but still slightly soft. Remove the eggs and set them aside.
Add the remaining 1 tablespoon of vegetable oil to the skillet. Add the diced carrots, peas, and chopped onion. Stir-fry for about 3-5 minutes, until vegetables are tender-crisp.
Add the minced garlic to the vegetables and cook for another 30 seconds, or until fragrant.
Add the cooked rice to the skillet with the vegetables. Pour the soy sauce and sesame oil over the rice. Stir everything together until rice is evenly coated and heated through.
Add the cooked chicken and scrambled eggs back into the skillet. Stir everything gently to combine.
Garnish with chopped green onions. Serve hot.