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Smash the garlic cloves, sprinkle with a pinch of the salt, and, with the flat side of a large knife, mash and smear the mixture to a coarse paste.
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Chop the cilantro into small pieces.
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Whisk the garlic paste, lime juice, cilantro and remaining salt and chili powder together in a bowl.
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Gradually whisk in the olive oil, starting with a few drops and then adding the rest in a steady stream.