Heat a large cast iron skillet over medium-high heat. Add the diced chicken with 2 tablespoons of butter, 1 tablespoon soy sauce, 1 tablespoon hibachi seasoning, salt, and pepper. Cook, stirring occasionally, until the chicken is browned and cooked through. Push to one side of the skillet.
Add the diced onion, minced garlic, frozen peas, and frozen carrots to the open side of the skillet. Add another tablespoon of butter and a little more hibachi seasoning. Sauté until the vegetables begin to soften, about 3 to 4 minutes. Push to the side with the chicken.
Crack the eggs into the cleared space in the skillet. Season with salt and pepper and scramble until just cooked through. Push to the side.
Add the remaining tablespoon of butter to the skillet followed by the day-old rice. Add 1 to 2 tablespoons of soy sauce and additional hibachi seasoning to taste. Let the rice cook undisturbed for 2 to 3 minutes until hot and slightly toasted on the bottom.
Mix everything together and let cook for another 2 to 3 minutes so the flavors come together completely.
Top with sliced green onions and serve hot with yum yum sauce drizzled over the top if desired.