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1
Combine the flour, sugar, salt, and lemon zest in a large bowl. Add the eggs and rum and work the mixture with the hands or a dough scraper until a shaggy mass forms. Add the softened butter in pieces and continue working until the dough is smooth, supple, and pulls cleanly from the bowl — it will not be sticky. The dough should feel silky and yield to light pressure without tearing.
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2
Shape the dough into a flattened disc, wrap tightly, and rest at room temperature for a minimum of 2 hours. The dough is ready when it yields without resistance to the heel of the hand and, when a small piece is stretched, does not spring back. Insufficient rest will render rolling to the required thinness impossible.
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3
Divide the rested dough into four pieces. Working one piece at a time on a lightly floured surface, roll to 1 mm or less — near-transparency. This is where the dish lives or dies: a sheet thicker than 1 mm will yield a bready, doughy fritter; at true thinness, the finished bugne will blister dramatically and shatter on the bite. Hold the sheet up to a light source; the hand should be faintly visible through it.
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4
Cut the rolled sheet into rectangles of approximately 15 × 6 cm. Make a single lengthwise slit down the centre of each rectangle, stopping 2 cm short of each end. Take one short end of the rectangle and pass it through the slit, drawing it through completely to form the characteristic twisted ribbon. Lay the shaped bugnes on a lightly floured tray.
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5
Heat the oil in a deep, heavy pan to exactly 170 °C, confirmed with a thermometer. Fry no more than three bugnes at a time to maintain the temperature. Lower each bugne gently into the oil; within seconds it will puff and blister across its surface. Fry 30–40 seconds per side. The bugne is done when it is pale gold, rigidly set, and covered in large, hollow blisters — not amber, not pale cream.
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6
Lift the bugnes with a spider or slotted spoon and drain on a paper-lined tray. Dust generously with icing sugar while still hot so the sugar adheres. The bugnes are ready to serve immediately; they hold their absolute crispness for no more than 6–8 hours.