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Put all the ingredients from the tomato juice down to and including the garlic in a pot that's at least 6 litres / quarts big.
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Bring to a boil, then lower to a simmer, cover and let simmer for about 45 minutes or until onion is soft. Stir from time to time to ensure there is no scorching.
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Put mixture through a food mill, using fine screen.
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Put sauce in pot or pan with a very wide surface area to speed evaporation -- Ball suggests even a wide skillet.
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Bring to a boil, then reduce to a simmer and let simmer until it reaches a consistency you are happy with. To get the 4 jars that Ball says the recipe yields, that should be about 30 minutes, until it's the consistency of a thin ketchup.
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Wash and chop cilantro, stir in.
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Adjust taste if desired with dry seasonings.
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Jar size: half-litre / pint or smaller.
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Put hot sauce into heated jars.
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Leave 2 cm (1/2 inch) headspace.
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Debubble, adjust headspace.
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Wipe jar rims.
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Put lids on.
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Process in a water bath canner or steam canner.
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Process jars for 40 minutes. Increase time as needed for your altitude.