Heat the butter in a large frying pan over medium heat and sauté the onions until soft.
Add the diced chicken to the pan, season with salt and black pepper, and cook until no longer pink.
Mix in the cooked rice, sesame oil, ketchup, and Worcestershire sauce. Cook, stirring frequently, until the rice is heated through and evenly coated with the sauce.
Stir in the cooked mixed vegetables and cook for another minute. Remove from heat and set aside.
In a bowl, beat the eggs lightly. Heat a nonstick frying pan over medium heat, add a little butter, and pour in half of the egg mixture.
Tilt the pan to spread the eggs into a thin layer. When the edges start to set, place half of the rice mixture in the center of the egg. Fold the egg over the rice to cover it completely.
Carefully slide the omurice onto a plate. Repeat with the remaining eggs and rice.
Drizzle with additional ketchup when serving.