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Combine all the ingredients except the ground black pepper in a 2 1/2-quart, heavy-bottomed, non-reactive saucepan. Stir well to combine and place the pan over medium heat, with the cover ajar. Bring the mixture to a full simmer, stirring occasionally, and then turn the heat to low. Continue to simmer until the sauce is thickened and the color deepens considerably, about 30 minutes, stirring occasionally (see below). Uncover, stir in a generous amount of freshly ground black pepper, and remove the saucepan from the heat. Let the sauce cool, uncovered, until just warm. If making a doubled or tripled amount, simmer the sauce for 45 minutes. (While cooling, lay a clean kitchen towel over pan to prevent debris from falling into the sauce.)
Pour the sauce through a triple-mesh wire sieve that’s positioned over another bowl and, using the flat edge of a sturdy rubber spatula, or a wooden spatula, force the sauce through, leaving the onions, garlic and peppers behind. Discard the solids, pour the sauce into jars, and affix their lids. Store the sauce in the refrigerator.
This sauce can be fully assembled and stored in the refrigerator for 6 months.