Boil 20 minutes, uncovered, then press through sieve or food mill.
Spray a large skill lightly with cooking spray. Add ground beef, let cook 3 to 5 minutes till it starts releasing juices.
Add the onion, green pepper, and mushrooms (optional). Let cook, stirring frequently, until onion is translucent and the mushroom slices have shrunk. Add to the tomatoes.
Add the seasoning from the oregano down to the black pepper.
Bring to a boil, then lower to a simmer and let simmer uncovered until reduced by half. This will take 2 to 3 hours, so you may want to do this at off-peak rates if they apply where you live.
Adjust seasoning to taste.
Ladle into either half-litre (1 US pint) OR 1 litre (1 US quart) jars.
Leave 3 cm (1 inch) headspace.
Wipe jar rims.
Put lids on.
Put in pressure canner.
Processing pressure: 10 lbs (69 kPa) weighted gauge, 11 lbs (76 kpa) dial gauge (adjust pressure for your altitude when over 300 metres / 1000 feet)