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1
Bring a large pot of well-salted water to a full rolling boil. Cook the conchiglie according to the packet time, stopping 1 minute short of done. Reserve 100 ml of pasta water before draining. The pasta is ready when it offers distinct resistance at the centre.
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2
While the water comes to the boil, warm the olive oil in a wide sauté pan over medium heat. Add the garlic and cook, stirring, until it turns an even pale gold and the oil is fragrant. Do not allow it to brown further.
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3
Pour in the white wine and let it bubble vigorously, scraping the pan, until reduced by exactly half. The sharp alcohol smell softens to a rounded, slightly sweet vapour — this is the moment to proceed.
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4
Add the halved Pachino tomatoes and the rinsed capers. Cook over lively heat for 5 minutes only, stirring occasionally. The tomatoes must soften and release their juices while retaining their acidity and freshness — they should look collapsed but still bright, not jammy.
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5
Remove the pan from the heat entirely. Add the drained conchiglie and toss to marry pasta and sauce, adding a splash of reserved pasta water if the pan looks dry. Then add the tuna cubes and toss continuously for 90 seconds maximum — this is where the dish lives or dies: the residual heat of the pasta and sauce is sufficient; the tuna must remain pink at the centre. Any further cooking destroys both texture and freshness.
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6
Scatter the torn basil over the pan and finish with a thread of raw extra-virgin olive oil. Serve immediately — the dish does not hold.