Prepare a pressure canner, along with jars, lids, and rings. For most canners, this means adding 2 to 3 inches of water and bringing it up to around just simmering (around 180 degrees F). Follow the instructions on your particular brand of pressure canner.
Chop the potatoes into 1/2 inch dice and weigh out 4 1/2 lbs. Remove the kale ribs and weigh out 1 lbs.
Brown the sausage over medium heat, stirring occasionally. This should take about 8 to 10 minutes.
Add the prepared vegetables, seasoning, salt and broth or water.
Bring to a simmer and cook for 5 minutes until everything is heated through.
Remove from heat and ladle the soup into prepared jars, leaving 1'' headspace.
Once filled, de-bubble jars, adjust headspace, and then cap the jars with 2-part canning lids and seal with rings to finger tight.
Load the jars into the canner on your canning trivet and add the lid. Turn the heat up to high.
Allow the canner to vent steam for 10 minutes, then seal the canner and bring it up to pressure. (Follow the instructions on your canner.)
This soup is canned at 10 pounds of pressure at sea level, but you'll need to adjust for altitude if you're about 1,000 feet in elevation. *see notes
Process jars for 75 minutes for pints and 90 minutes for quarts.