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1
Peel the outer papery skin from each lampascione and trim the base, removing only what is necessary — the bitter compounds are distributed throughout the bulb. Bring a generous pot of salted water to the boil, add the lampascioni, and boil for 10 minutes. Drain, cover with fresh salted water, and boil a second time for 10 minutes. Drain and pat dry. The bulbs should still carry a distinct bitter note; a completely de-bittered lampascione has lost its character.
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2
Warm the olive oil in a wide pan over medium heat. Arrange the lampascioni in a single layer — do not crowd the pan, or they will steam rather than take colour in the sauce. Add the wine vinegar and honey, stir once to combine, and cook at a steady medium heat for 10 minutes, turning the bulbs occasionally. This is where the dish lives or dies: the sauce must reduce and coat each bulb in a glossy sweet-sour glaze without the lampascioni softening to mush — they must remain firm to the bite.
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3
Remove from the heat and allow to cool to room temperature — the flavour is more complex when the dish is not served cold. Scatter mint or parsley leaves over the surface immediately before serving.