First things first, you want to sanitize your jars, lids and rings in the dishwasher or in hot, soapy water by hand. Since you'll be processing them for over 10 minutes, you don't need to sterilize them. Leave the jars in the hot water until you are ready to use them.
After you've prepped all of your vegetables, place them into a large stock pot along with the 12 cups of water and salt and pepper, and boil for 5 minutes.
Next, ladle the hot soup into the hot jars and leave about 1” of headspace at the top. Make sure each jar is half-full of solids – this is important!
Remove any air bubbles with a butter knife.
Place the lids and rings on the jars and screw them on tightly.
Process the pint-sized jars for 60 minutes and quart-sized jars for 75 minutes at 10 pounds of pressure in a pressure canner if you have a weighted-gauge canner, or at 11 pounds of pressure for a dial-gauge canner. These need to be adjusted for altitude. See table below.
Remove jars from canner, set aside to cool. You will hear popping sounds, this is a good thing, it means the processed jars are sealed.
After 24 hours, inspect the jars for signs of spoilage. Store the good ones in the pantry, and eat or place the failed jars in the fridge for consumption.