I just cut up the sausage and cooked it with olive oil in the pot (andouille isn't very greasy so I added extra oil) while that got started I chopped up some carrots, celery, onion and some boiled potatoes I had lying around and put them in the pot too.
When they were soft I added the beans and their liquid, some extra water and a few teaspoons of chicken "Better Than Bouillion." I let it all cook for a bit - 20 or 30 minutes. I wasn't paying attention. I decided it was cooked enough, turned the heat off and stirred in the prepped kale. Easy peasy.
When you make sausage soup the sausage does all the work. Get good sausage. Some barley, rice or other grain would probably be good in there too.