Add everything except the final three ingredients to the slow cooker.
Cover and cook on high for 3-4 hours or low for 5-6 hours, until the sausages are cooked through and the vegetables are tender.
Use kitchen shears to cut the sausage links into bite-sized pieces directly in the slow cooker. Or remove the sausages and cut them into rounds and add back to the sauce.
Stir in heavy cream and grated parmesan cheese until well combined and creamy.
Meanwhile, cook the pasta according to the package instructions. Drain and toss with a drizzle of olive oil to prevent it from sticking.
Serve the creamy sausages over the cooked pasta and garnish with extra parmesan if desired. Alternatively, add the cooked pasta to the slow cooker and toss together before serving.