Heat one tablespoon of neutral oil in a medium saucepan over medium heat. Add the shallot and cook until caramelized.

Add the remaining vegetables and sauté for one to one and a half minutes. Add the tomato paste and cook for 30 seconds, stirring constantly.

Deglaze the pan with the red wine and cook until reduced by half.

Add the beef broth, reduce the heat to a simmer, and cook for 20-30 minutes, or until reduced by about two-thirds.

Meanwhile, melt the butter in a clean small saucepan. Add the flour and stir with a spatula until golden to create a roux. Remove from the heat and let cool slightly.

Place a fine-mesh strainer over the pan with the roux. Strain the reduced broth directly into the roux, pressing the vegetables with the back of a spoon to extract as much liquid as possible. Discard the solids.

Return the pan to the heat and gently whisk until the sauce is thickened, glossy, and coats the back of a spoon. Taste and season with freshly ground black pepper as needed. Set aside and keep warm.

Heat two tablespoons of neutral oil in a deep-sided frying pan or wok over medium-high heat.

Add the diced chicken and cook, tossing occasionally, until lightly browned and cooked through.

Add the onion and mushrooms and cook until the onion is translucent.

Push the chicken and vegetables to one side of the pan. Add the ketchup to the empty side and cook briefly to caramelize.

Stir in the Worcestershire sauce, then add the rice. Use a spatula to break apart the rice as it cooks, stirring until the grains are evenly coated.

Add the butter and season with salt and freshly ground black pepper to taste.

Stir in the chopped parsley and set aside.

Heat an eight-inch nonstick frying pan over medium heat. The pan should be hot but not smoking.

Pour in the beaten eggs. Working quickly, use chopsticks or a spatula to stir the eggs, continuously moving the cooked portions toward the center.

When the eggs are about 70% set but still wet on top, stop stirring and let them cook for about five seconds to set the base.

Tilt the pan and use chopsticks or a spatula to roll the omelet into an oval, bringing the top and bottom edges together in the center.

Gently flip the omelet so the seam is facing down. Cook for a few seconds to seal the seam.

Pack the fried rice into an omurice mold or small bowl. Invert it onto a serving plate and remove the mold.

Using chopsticks or a spatula as a guide, gently slide the omelet on top of the rice.

Using a sharp knife, slice the omelet lengthwise down the center, allowing the soft interior to open and fall over the rice.

Ladle a generous amount of warm demi-glace over the omelet.

Garnish with additional chopped parsley and serve immediately.