Remove cores and coarsely chop the tomatoes, spread out on a foil lined cookie sheet and lightly brush with the olive oil. Broil in the oven until the skins begin to wrinkle and darken for approximately 10 minutes. Turn as needed to evenly roast and prevent sticking. Remove from oven and cool briefly.
Pick out as many of the large pieces of tomato skin that you can using fingers and then run the tomatoes through a tomato mill to remove remaining skins and seeds. If you have no objections to skins and seeds in your sauce just puree in a blender or food processor.
Pour sauce into a large pot and combine with the remaining ingredients (do not use aluminum pot). Cook over low-medium heat, stirring frequently, until the celery and peppers are soft and sauce is the desired thickness. We prefer a somewhat thinner sauce so only cook it for about 30 min.
Ladle hot sauce into hot pint jars taking time to evenly distribute the chunky vegetables. Leave 1" headspace, remove any air bubbles, wipe rims, and apply 2 piece lids and bands.
Process pints 20 minutes at 10 lbs. pressure (adjust for your altitude) in a pressure canner.
Serve heated over pasta of your choice. This also makes a good sauce for crockpot meat dishes such as Swiss Steak or as an additive to meatloaf.