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1
Make the ketchup fried rice. Set a wok or wide skillet over high heat until smoking. Add the oil, then the diced chicken; cook, tossing, until the surface of the chicken is opaque and beginning to colour at the edges. Add the onion and continue tossing until softened and translucent. Add the cold rice, breaking up any clumps against the pan. Pour in the ketchup and fold it through the rice until every grain is uniformly coated and the mixture is fragrant with a lightly caramelised tomato smell. Season with salt. The rice is ready when it moves freely in the pan without sticking and the ketchup smell has deepened from raw to sweet and slightly concentrated.
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2
Cook the hayashi rice sauce. Melt the butter in a wide, heavy saucepan over medium-high heat. Add the sliced onions and cook, stirring frequently, until deeply golden and collapsed — they should be the colour of caramel and sweet-smelling. Add the beef slices and cook until no pink remains. Pour in the red wine and reduce by half; the sharp alcohol smell will give way to a rounded, fruited aroma. Add the stock, ketchup, and Worcestershire sauce. Simmer uncovered over low heat, stirring occasionally, until the sauce coats the back of a spoon and leaves a clear track when a finger is drawn across it. Season. The sauce is done when the surface shows slow, heavy bubbles and the colour is a deep mahogany brown.
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3
Rest the hayashi rice. If time permits, cool the sauce completely and refrigerate overnight. Reheat gently before service. The sauce is ready to serve when it is uniformly glossy and the surface shimmers without separation.
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4
Form the omurice omelette — this is where the dish lives or dies. Heat a small (20 cm) omelette pan until the surface is at maximum domestic heat — a drop of water should skitter and vanish immediately. Add the oil. Pour in the two beaten eggs for one portion. Working with chopsticks or a spatula, fold the egg rapidly from the edges toward the centre for 8–10 seconds only: the exterior must set into a pale gold skin while the interior remains liquid and flowing. Lay the mound of ketchup rice in the centre of the omelette, then fold or roll the egg over the rice to enclose it, tipping the pan to assist. The omelette should bulge softly from its liquid interior; any browning or fully set texture indicates the heat was insufficient or the timing too long.
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5
Plate and serve both dishes. For the omurice: invert the omelette-wrapped rice onto a warmed plate so the seam faces down. At the table, draw a single knife slash along the crown of the omelette lengthways; the interior should open and flow as liquid egg over the rice. For the hayashi rice: mould hot plain rice into an oval on a warmed plate and ladle the sauce generously alongside or over. Both dishes are served immediately.