In a large stockpot, heat a tablespoon of oil over medium heat. Add the chopped onions, celery, carrots, and garlic. Sauté until the vegetables are tender, about 5–7 minutes.​

Stir in the diced potatoes, broth, basil, parsley, salt, and pepper. Bring the mixture to a boil, then reduce heat and simmer until the potatoes are tender but not mushy, approximately 15–20 minutes.​

If using, add diced ham or cooked bacon to the soup. For a thicker consistency, mix ClearJel with a small amount of cold water to create a slurry, then stir it into the soup. Simmer for an additional 5 minutes to activate the thickener.​

While the soup is simmering, sterilize your Mason jars and lids by boiling them in water for 10 minutes. Keep them hot until ready to use. Fill your pressure canner with the appropriate amount of water as per the manufacturer’s instructions and begin heating it.​

Using a funnel, ladle the hot soup into the hot jars, leaving 1 inch of headspace at the top. Remove any air bubbles by running a bubble remover or spatula around the inside edge of the jar. Wipe the rims clean with a damp cloth, place the lids on, and screw on the rings until fingertip-tight.​

Place the filled jars into the pressure canner. Lock the lid and bring the canner to the required pressure: 10 pounds for weighted-gauge canners or 11 pounds for dial-gauge canners. Process pint jars for 75 minutes and quart jars for 90 minutes.​

After processing, turn off the heat and allow the canner to depressurize naturally. Once depressurized, carefully remove the jars and place them on a towel-lined surface. Let them cool undisturbed for 12–24 hours. Check the seals, label the jars with the date, and store them in a cool, dark place.​