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1
Pour the olive oil into a wide, heavy pan set over low heat, then add the onion and garlic. Sweat gently for 15 minutes, stirring occasionally, until completely soft, translucent and fragrant — keeping the heat low so the onion melts into sweetness rather than taking on any colour that would make the finished dish bitter. The moment the onion turns golden, that edge of bitterness is already locked in.
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2
Seed the peppers, cut them into broad strips, and add them raw to the softened onion, stirring to coat each strip in the oil before adding the chopped tomato and seasoning with salt. Cook over low-to-medium heat, stirring occasionally, for 45 to 60 minutes, keeping the heat low enough that the peppers collapse slowly and evenly into a silky, almost jam-like mass — a rushed, hotter pan will scorch the edges while the centres stay fibrous and raw-tasting. The peppers are ready when they offer no resistance and the oil has pooled, glossy and sweet-scented, around the collapsed flesh.
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3
With 10 minutes of cooking remaining, add the wine vinegar and stir it through, then continue cooking uncovered so that the sharp edge of the acid has time to soften and marry into the peppers rather than sitting raw against their sweetness. The pan will smell sweet and faintly acidic when the balance is right.
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4
Remove the pan from the heat, then tear the basil leaves over the surface and fold them in gently, working off the heat so the leaves stay bright green and release their fresh aroma into the warm oil rather than wilting to a dark, bitter shadow of themselves. The contrast between the basil's fragrance and the deep sweetness of the peppers is what lifts the whole dish.
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5
Allow the peperonata to cool to room temperature before serving, so the oil, juices and vinegar have time to settle back through the collapsed flesh and the flavours read as one rather than separate. The surface should be glossy with oil, the peppers fully collapsed and deeply coloured; serve as a contorno or antipasto with crusty bread.