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1
Place the olive oil in a wide, heavy pot over a medium flame and add the onion, celery and carrot. Cook, stirring regularly, until the soffritto is completely softened and the onion is translucent — not browned — because colour here means bitterness that will carry through every spoonful of the finished soup. The vegetables should be yielding and fragrant before you move on.
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2
Add the tomato passata and stir to combine with the soffritto. Cook for several minutes, stirring, until the tomato has darkened slightly and lost its raw, acidic edge — the smell shifts from sharp to round, which tells you the passata has cooked into the fat rather than merely sitting on top of it.
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3
Add the potatoes, green beans and zucchini, then pour in the water or light vegetable broth. Stir in the saffron dissolved in warm water — dissolving it first rather than dropping it in dry ensures the colour and perfume spread evenly through the broth rather than concentrating in patches. Bring to a gentle simmer and cook until the vegetables are almost — but not fully — tender; the potatoes should still offer a little resistance at the centre.
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4
This is where the dish lives or dies: add the fregola only when the vegetables are nearly done, because if added too early the fregola absorbs excess liquid and turns mushy, and if too late it remains chalky and the broth is not thickened by its starch. Stir in the fregola and cook at a steady simmer for 15–18 minutes, adding boiling water as needed — boiling rather than cold so the simmer is never broken and the fregola cooks evenly — to maintain a soup, not a porridge, consistency. The fregola is done when each sphere is tender throughout yet holds its shape, the broth has thickened noticeably from released starch, and the soup is a deep golden colour from the saffron.
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5
Season with salt, tasting to ensure the seasoning carries through the starch. Remove from the heat and finish with a generous drizzle of raw Sardinian extra-virgin olive oil directly into the pot, so its fruity-bitter character is not cooked off and remains a distinct note against the soup. The surface should glisten.