Heat 1 tbsp vegetable oil in a large skillet over medium to medium-high heat.
Add the chicken to the skillet in a single layer.
Cook the chicken for approximately 2 minutes per side, or until browned and cooked through.
Add additional vegetable oil as needed to prevent sticking.
Transfer the cooked chicken to a plate.
Cover the chicken to keep it warm and set aside.
Add 1 tbsp vegetable oil to the same skillet over medium to medium-high heat.
Add the finely chopped onion, finely chopped carrots, and frozen peas.
Cook the vegetables, stirring several times, until they are crisp-tender.
Reduce the heat to low.
Add the minced garlic.
Cook for 1 minute, stirring constantly to prevent the garlic from burning.
Transfer the cooked vegetables to a plate and cover to keep warm.
In a small bowl, whisk the eggs until evenly combined.
Add 1/2 tbsp butter to the same skillet over low heat.
Pour the whisked eggs into the skillet.
Cook the eggs just until set, stirring gently as needed.
Remove the eggs from the skillet and add them to the plate with the cooked vegetables.
Cover to keep warm.
Add the remaining butter to the skillet and melt over medium heat.
Add the cooked and chilled long grain white rice to the skillet.
Break apart any large clumps of rice with a spoon or spatula.
Drizzle the rice with 3 tbsp low-sodium soy sauce to start.
Increase the heat to medium-high.
Fry the rice until lightly browned, stirring several times but not continuously, to allow the rice to develop color and texture.
Work in batches if the skillet is crowded.
Add additional soy sauce, 1 tbsp at a time, if more flavor is desired.
Drizzle the rice with sesame oil.
Add the chopped green onions.
Stir until evenly combined.
Return the cooked chicken, vegetables, and eggs to the skillet.
Stir gently until all ingredients are evenly distributed.
Continue cooking until the chicken, vegetables, eggs, and rice are heated through.
Taste and season with salt and pepper, if desired.
Serve warm as a main dish or side dish.