Wash and prepare the tomatoes by dipping them in boiling water, then cooling in cold water to remove the skins.
Quarter the tomatoes and boil them in a large saucepan for 20 minutes. Pass through a food mill or sieve to create a pulp.
In a skillet, brown the ground meat. Add garlic, onions, celery or green peppers, and mushrooms, sautéing until tender.
Combine the meat and vegetable mixture with the tomato pulp, adding salt, oregano, parsley, black pepper, and brown sugar. Bring to a boil, then simmer until thickened.
Fill jars, leaving a 1-inch headspace, and wipe the rims and cap with 2 part canning lids.
Load the jars into the canner, seal the lid, and allow the steam to vent for 10 minutes.
Bring the canner up to pressure and process pint jars for 60 minutes and quart jars for 70 minutes. Pressure is adjusted to altitude, but the process times are always the same. See altitude adjustments for pressure below.
Cool the jars on a towel, check the seals, and store in a cool, dark place.