Drizzle some oil into a medium pot or Dutch oven set over medium-high heat, squeeze the sausages out of their casings and cook, breaking up with a spoon, until no longer pink.
Add the celery and carrot and cook for 3-4 minutes, until starting to soften.
Add the stock, bring to a simmer, add the pasta and cook for 10-15 minutes, or until the vegetables and pasta are tender.
Stir in the beans and kale, stirring until it wilts.
Serve with Parmesan grated on top.