First, make the demi-glace sauce. In a saucepan, melt half the butter over medium heat. Fry the onions until translucent then add sliced mushroom and brown. Set aside.
In a separate saucepan melt the other half of the butter over medium heat. Add the flour and whisk constantly until a smooth paste forms. Gradually pour in the broth, whisking continuously to avoid lumps. Stir in the ketchup, soy sauce, Worcestershire sauce, salt, and pepper and sugar. Simmer the sauce for a few minutes until it thickens to a silky consistency.Set aside while you cook the rice and egg.
Fry the rice
In a large skillet or pan, heat the butter over medium heat. Add the chopped onions and sauté until translucent.
Add the mixed vegetables and cook for a few minutes until tender. Stir in the cooked rice, ketchup, soy sauce, salt, and pepper. Mix well, ensuring the rice is evenly coated with the seasoning. Cook for a few more minutes, stirring occasionally, until the rice is heated through. Set aside and wipe out the skillet to use for cooking the egg.
Make the omelette
In a bowl, whisk the eggs, salt, and pepper until well combined. Return the skillet to a medium heat, add the vegetable oil, and swirl to coat the pan evenly.
Pour half of the egg mixture into the skillet, tilting it to spread the egg evenly. Cook until the bottom is set but the top is still slightly runny. Spoon half of the fried rice onto the centre of the omelette. Fold the omelette over the rice, creating a half-moon shape. Slide it onto a plate.
Repeat the process to make the second omelette.
To serve, place your Omurice on a plate, and generously drizzle the demi-glace sauce over the top.
Tip
Customise the fried rice with your favourite ingredients, such as diced chicken, shrimp, or mushrooms. The umami-rich demi-glace sauce adds depth and richness to the dish, elevating it to a true Japanese comfort food classic.