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Put the onions, garlic, and hot pepper in a pot with a little olive oil, just to get the flavours going, then put in everything else except basil and 1Tbsp olive oil.
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Over medium heat, get the sauce bubbling, then simmer uncovered, stirring about every five minutes to make sure it doesn’t stick. I simmered it for about an hour to reduce it a fair bit. Depending on kitchen environment, this could be faster or slower.
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When you like the consistency, stir in the basil leaves.
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Using a food processor or immersion blender, blend the sauce to make a nice consistency, then stir in the olive oil. (If you like a chunky sauce, skip this step.)