Heat vegetable oil in a large non-stick skillet or wok over medium-high heat. Once the oil is hot, add the chicken and cook until the chicken is no longer pink. Transfer the chicken to a plate and set it aside.
Melt butter in the skillet. Add eggs and scramble until just set. Transfer eggs to a plate and set aside.
Add toasted sesame oil and frozen peas and carrots mix, and green onions to the skillet and sauté for about a minute. Stir in the garlic and cook for another minute.
Add the cooked chicken and scrambled eggs back to the pan, then stir in the rice. Drizzle with soy sauce and season with kosher salt and black pepper to taste. Cook for 3 to 5 minutes, until warm.