Make the demi-glace sauce. Combine the ketchup, soy sauce, Tontaksu sauce, honey or sugar, water, and milk in a large bowl. Set aside.

Heat the oil in a frying pan on medium-high heat and add the flour. Cook and stir until the mixture turns dark brown (5-7 minutes). Be careful not to burn it.

Pour in the sauce mixture, stir, and bring the heat to medium. Let the sauce simmers, stirring, for 8-10 minutes until it thickens. Once thickened, set aside.

Make fried rice. Preheat a pan to medium-high. Add chicken and cook for 2-3 minutes. Add butter, onions, mushrooms, and pepper, and cook until tender.

Add the warm rice, toss to incorporate, and pour the ketchup into the pan. Let it come begin to bubble and then toss it to incorporate. Cook for 1-2 minutes.

Turn off the heat and cover the rice to keep it warm.

Prepare the omelettes. Whisk the eggs with a little salt and pepper to taste.

Strain the eggs. Incorporate the cream. Don’t over-whisk. Let the mixture rest.

Heat some oil, and pour a quarter of the egg mixture. Scramble it with chopsticks from the outside to the inside.

Place a serving of the fried rice on the undercooked omelette. Let it cook for 30 seconds, then fold the opposite edges to the center to cover the rice. Flip the omelette with the spatula, and allow it to cook for a few seconds to seal.

Transfer the omelette to a plate and further shape it with paper towels if desired.

Top the omurice with demi-glace sauce or ketchup and some parsley. Enjoy!