Melt the butter in a large pot over medium high heat. Saute onions and carrots and a little salt and pepper for a few minutes until soft and tender.
Add potatoes, broth, and sausage to the pot. Season with salt and pepper.
Cover and simmer for 20 minutes until the potatoes are very tender. Remove the sausage and puree the potatoes with a stick blender until the soup is nice and thick but still has a few chunks of potatoes.
Add the sausage back to the pot.
Serve and enjoy!