In a bowl, combine ketchup, chicken broth, and soy sauce until well mixed.

Heat vegetable oil in a skillet over medium heat. Sauté the mushrooms for about 5 minutes until golden brown.

Add onions, carrots, and peas, and cook for 3 minutes until softened.

Incorporate cold leftover rice, breaking it up gently, and mix with the sauce. Season with salt and pepper, and remove from heat.

Whisk eggs with water and a pinch of salt in a separate bowl.

Heat oil in another skillet, pour in the egg mixture, and cook until mostly set but slightly runny.

Plate the fried rice and cover it with the omelette or fold the omelette over the rice.

Drizzle with additional ketchup before serving.