Combine all ingredients except tomatoes in a large heavy-bottom pot; bring to a boil over medium heat. Reduce heat to low and simmer, stirring occasionally, until vegetables are tender, about 10 minutes.
Stir in tomatoes, raise heat to medium and bring to a boil. Reduce heat to low; simmer until mixture begins to thicken, stirring frequently, about 30 minutes.
Using an immersion blender, puree until smooth. Mixture will be thin. (Alternatively, remove pot from heat, let mixture cool slightly and puree it in batches in a blender.) Return mixture to pot, return pot to heat and boil over medium heat until very thick, stirring frequently to prevent scorching, 2 to 2 1/2 hours longer. Ketchup is ready when a dollop spooned onto a plate does not weep liquid. (Cooking time might vary based on width of pot and juiciness of tomatoes.)
Ladle ketchup into prepared half-pint canning jars, leaving 1/4 inch of headspace, and process for 15 minutes using the boiling-water method (see below).
Don't be intimidated: Getting the right seal to keep food fresh is as easy as boiling water.
STEP Put the rack in a large pot. Arrange empty jars, open side up, in a single layer. (Arrange a full layer, even if you are planning to use only a few, to keep jars from tipping over.) Add cold water to the pot until there is at least 2 inches of water above the jars' rims. Set the pot over high heat, cover it and bring water to a boil. Put lids, white side down, in a large bowl.
Step Prepare recipe as directed up until the ladling step (keep hot until ready to place in jars). Reduce heat under the pot so water is hot but not boiling.
Step Using canning tongs, remove a jar of hot water from the pot. Pour it over the lids in the bowl. Set the jar on a clean kitchen towel. Remove 2 more jars, pouring the water back into the pot, and set them on the towel.
Step Insert the funnel into the first jar. Carefully ladle the hot food into the funnel, keeping the headspace--the distance from the top of the mixture to the top of the jar--indicated in the recipe.
Step Swipe a bubble tool between the mixture and the inside of the jar to release any air bubbles, adding more of the mixture if necessary to achieve the proper headspace. Repeat with remaining food and jars.
Step Use a clean kitchen towel dipped in hot water to carefully clean the rim of each jar. Use soft-tipped tongs, a lid lifter or your fingers to retrieve a lid from the bowl and center it on the jar. Screw the ring on the jar with your fingertips, taking care to make it tight enough to stay centered but not so tight that you won't get a vacuum seal. Repeat until you have filled the jars.
Step Use canning tongs to lower filled jars into hot water. Be sure jars are covered by 2 inches of water. Cover the pot and return to a boil. Begin counting your processing time when the water is boiling. When the time is up, turn off heat, remove pot lid and allow the jars to rest for 5 minutes.
Step Using canning tongs, remove the jars to a towel-covered surface. Let rest for 24 hours. To test the seals, remove the rings and gently push up on the lids. If they stay in place, the food is safe to store for up to a year in a cool, dark place. If the lids don't stay put, refrigerate the jars and eat the contents soon.