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1
Combine the raisins, onions, garlic, tomato paste and 1/3 cup vinegar in the container of a food processor; process the mixture until smooth, and then transfer the mixture to a large, heavy saucepan.
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2
Add the banana chunks and another 1/3 cup vinegar to the food processor container; process the mixture until smooth and then transfer the banana mixture to the saucepan.
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3
Add the remaining 2/3 cup vinegar, 3 cups water, brown sugar, salt and cayenne pepper.
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4
Bring the mixture in the saucepan to a boil over medium-high heat, stirring frequently.
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5
Reduce the heat to low and cook the ketchup, uncovered, stirring occasionally, for 11/4 hours.
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6
If the ketchup threatens to stick to the bottom of the pan at any point, add some of the remaining water, up to 1 cup.
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7
Add the corn syrup, allspice, cinnamon, nutmeg, pepper and cloves to the ketchup.
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8
Cook the ketchup over medium-low heat, stirring frequently, for 15 minutes longer, or until it is thick enough to coat a metal spoon.
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9
Stir in the rum.
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10
Remove the ketchup from the heat and let it cool a few minutes.
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11
Force the ketchup through a fine sieve to strain it, pressing down hard on the solids.
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12
Remove the ketchup from the heat and let it cool to room temperature.
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13
Store covered, in the refrigerator, for up to 1 month.