Process tomatoes, green peppers and onions in batches in a blender, add to a large stockpot. Bring to a boil, boil gently for one hour. Stir in tomato paste and next 8 ingredients; boil one more hour. Remove and discard bay leaves.
Spoon into hot sterilized jars, leaving 1/2-inch headspace. Add one tablespoon balsamic vinegar to each jar. Remove air bubbles, wipe jar trims. Cover at once with metal lids and screw on bands. Process in a boiling water bath 20 minutes; set jars on a towel to cool.