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1
Drain the soaked chickpeas and place them in a large, heavy pot. Cover with cold water by at least 8 cm. Add the garlic, bay leaves, and rosemary. Bring to the gentlest possible simmer over medium heat, then reduce immediately to low. Cook uncovered for 30 minutes. The chickpeas will still be firm at the centre.
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2
Drain the soaked chestnuts, discarding their soaking water, which may carry bitterness. Add the drained chestnuts to the pot. This is where the dish lives or dies: the staggered addition — chickpeas first, chestnuts after 30 minutes — is the single step that determines whether both components arrive at tenderness together. Maintaining a bare simmer throughout prevents the chestnuts from breaking apart before the chickpeas soften. Vigorous boiling at any point will sacrifice one component to the other.
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3
Continue at a bare simmer for a further 40–50 minutes, adding hot water as needed to keep the ingredients just submerged. Do not season. The soup should thicken gradually as the chestnuts release their starch; some natural breakdown of both components is correct and desirable. The texture sought is roughly whole pieces in a porridge-like broth, not a smooth purée.
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4
In the final 15 minutes of cooking, add the salt. Taste and adjust. Both chestnuts and chickpeas should yield completely without resistance when pressed between two fingers, while retaining their general shape.
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5
Remove and discard the garlic, bay leaves, and rosemary sprig. Ladle the soup into warmed bowls. Pour the raw olive oil generously over each portion and crumble the dried peperoncino directly on top. Both finishes are structural elements of the Basilicatan dish, not garnish. Serve immediately, or allow to rest — the soup deepens markedly the following day.