In a large Dutch oven or heavy bottom saucepan set over medium heat, heat up the chopped rhubarb with 1 cup of water. Bring the mixture to a simmer and let the rhubarb cook until the water is mostly absorbed and the rhubarb is a similar to a jam consistency, 10-15 minutes. Allow to cool, transfer to a large bowl, and set aside. Wipe down the Dutch oven.
Bundle the peppercorns, mustard seeds, bay leaves, cinnamon, allspice and cloves in a piece of cheesecloth and tie with kitchen twine securely, leaving about 5 inches of extra twine on one end.
Place the Dutch oven over medium heat and add the olive oil. Add the chopped onion and cook until soft, approximately 5 minutes. Stir in the tomato paste, garlic and cayenne and cook for an additional minute.
Transfer to a blender along with the rhubarb and tomatoes. Puree, in batches, if necessary, until smooth. Return the mixture to the pot and add the brown sugar, vinegar and salt. Submerge the the spice bag into the mixture and tie the long end of twine to the top of the pot.
Bring the mixture to a boil over medium-high heat, then reduce the heat to medium-low and simmer, stirring occasionally, until the mixture is darker, thick and reduced to about 4 cups, approximately 2 hours. If possible, use a splatter guard to help keep the liquid from bubbling out of the pot.
Remove the spice bag. Strain ketchup through a fine mesh strainer set over a large bowl, pressing on the solids. (For a smoother final product, press through a food mill). Let the ketchup cool to room temperature, then season with salt and pepper to taste.
Pour cooled ketchup into jars and refrigerate. Ketchup can be refrigerated for up to one month.