In a large pot or bowl, combine tomatoes, celery, onion, green pepper, and salt. Cover with a lid or large towel and let stand overnight. The next day, drain through a colander - do not press on the vegetables.
Place drained vegetables in a large pot. Add sugar, brown sugar, pepper, and vinegar. Tie pickling spices in cheesecloth and add to the pot. Bring to a boil, then reduce heat and simmer, uncovered, for 15 minutes.
If you plan to eat all the stewed tomatoes within 1 week, simply store it in a covered container in the fridge.
Freeze it in freezer-safe baggies or containers for up to 12 months.
Can it in jars for pantry storage. Ladle mixture into sterilized jars, leaving ½" of headspace. Place a lid on the jar and then a ring, just finger-tight. Process in a boiling water bath for 10 minutes. This will yield 5 to 6 pints. Best eaten within 12 months.
