place onions in a heavy bottom saucepan and add the vinegar, honey. salt,and pepper. bring to a simmer over medium heat and continue to simmer for about 15 minutes, stirring frequently, until the liquid has evaporated. Remove the pan from the heat and let cool.
transfer the cooled onion mixture to the bowl of a food processor and puree until smooth. add the ketchup and pulse several times until throughly incorporated. adjust the seasonings, transfer to an air tight container, and store in the refrigerator.