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1
Preheat the oven to 200 °C. Beat the egg yolks with the caster sugar and vanilla extract until the mixture is thick, pale, and falls in a continuous ribbon from the whisk — the ruban stage. The sugar must be fully dissolved and the volume noticeably increased.
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2
In a separate, scrupulously clean bowl, whisk the egg whites with the pinch of salt to stiff, glossy peaks. The peaks must hold their shape without collapsing when the whisk is lifted.
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3
Fold the whites into the yolk mixture in three additions. Add the first third vigorously to lighten the base. Incorporate the remaining two thirds gently with a spatula, cutting and folding until just combined — visible white streaks should remain. This is where the dish lives or dies: over-folding deflates the whites and produces a flat, dense omelette; the mixture must retain its soufflé lightness.
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4
Heat a 24 cm ovenproof pan over medium heat and melt the butter until it foams. Pour in the mixture and spread it gently to fill the pan without pressing down. Cook over moderate heat for 2–3 minutes until the underside is set and pale gold — a spatula drawn beneath the edge meets clean resistance.
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5
Transfer the pan immediately to the preheated oven. Bake for 6–8 minutes until the omelette has risen dramatically and the surface is golden. The centre should jiggle perceptibly when the pan is nudged — it must not be set firm throughout.
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6
Working without delay, slide the omelette onto a warm oval platter and fold it in half. It should crack slightly at the fold, revealing the mousse-like interior. Dust immediately with icing sugar and mark a crosshatch pattern with a red-hot poker or skewer — the sugar caramelises into crisp, darkened lines on contact.
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7
Warm the dark rum in a small pan until hot but not boiling, ignite it, and pour the flaming rum over the omelette at the table. The blue flame should dance freely across the sugared surface, burning off the alcohol and leaving a deep, caramelised rum perfume. Serve within 60 seconds alongside crème anglaise or fruit compote.