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1
Heat 3 tablespoons of extra virgin olive oil in a heavy saucepan over medium-low heat. Add the thinly sliced garlic and cook, undisturbed between gentle turns, for 3–4 minutes. The garlic is ready when each slice is pale gold, visibly intact, and the oil smells sweet and fragrant — stop before any edge shows brown.
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2
Add the tomatoes, olives, capers, and herb bouquet. Season with salt, black pepper, and the pinch of sugar. Stir once to combine and bring to a gentle simmer.
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3
Simmer uncovered for 30–40 minutes. This is where the dish lives or dies: do not stir the oil back into the sauce. The sauce is done when the tomatoes have broken down to a rough, rustic texture and golden pools of oil have risen freely to the surface — that separation is the signature of a properly made Provençale, not a fault to be corrected.
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4
Remove the herb stems. Take the pan off the heat entirely before proceeding — residual heat in the pan is sufficient. Add the basil chiffonade and the final drizzle of raw olive oil. The basil should remain a vivid, unoxidised green; any blackening means it was added while the sauce was still on the flame.