In a large stockpot or a preserving pot, combine the water, orange juice, onion, cinnamon stick and ginger root, and bring to a boil.
Lower the heat and simmer for 10 minutes.
Add the cranberries and return the pot to a boil.
Partially cover the pot, lower the heat to medium-low and simmer for 15 minutes, or until most of the cranberries have burst. Stir frequently to prevent scorching or sticking.
Slide the pan off the burners and let cool for 10 minutes.
Remove the ginger root and the cinnamon stick and discard.
Transfer mixture to a blender; add ground mustard seeds and puree.
Rinse the stockpot and lay a fine mesh sieve over it.
Pour the blended cranberry mixture into the sieve and use a wooden spoon to work the mixture through the sieve, making it perfectly smooth.
Add the remaining ingredients in the stockpot and bring to a boil over medium-high heat, stirring constantly.
Remove from heat.
Use a ladle to scoop the Cranberry Ketchup into half-pint (8-ounces) jars, leaving 1/2 inch of headspace. Use a chopstick to pop the air bubbles.
Moisten a paper towel with vinegar and wipe the rims of the jars clean.
Place lids on the jars and fasten appropriately.
Use canning tongs to transfer the jars to a canner full of boiling water that covers the jars by 2 inches.
Put the lid of the canner in place, return the water to a boil, and let it process for 15 minutes.
Carefully transfer the jars to a towel-lined counter or wire cooling rack and allow them to cool completely, preferably overnight, before removing any rings, wiping the jars clean and labeling.
Store the jars in a cool, dark place for up to 1 year. Once opened, it will be good for up to 3 weeks when stored in the refrigerator.