Wash tomatoes. Dip in boiling water 30–60 seconds or until skins split; dip in cold water, slip off skins, remove cores, and quarter.
Boil tomatoes uncovered 20 minutes, then press through a food mill or sieve.
Sauté onions, garlic, celery or green pepper, and optional mushrooms in vegetable oil until tender. Do not increase the tested vegetable proportions.
Combine vegetables and tomato pulp; add salt, oregano, parsley, black pepper, and brown sugar. Bring to a boil and simmer uncovered until thick enough for serving and reduced by nearly half, stirring frequently.
Fill hot jars, leaving 1-inch headspace.
Pressure can pints 20 minutes or quarts 25 minutes. Dial gauge: 11/12/13/14 psi at 0–2,000/2,001–4,000/4,001–6,000/6,001–8,000 ft. Weighted gauge: 10 psi at 0–1,000 ft and 15 psi above 1,000 ft.