Melt butter in a large soup pot over medium heat. Add onion, celery, carrots, thyme, and parsley. Cook 5 minutes.
Add potatoes, sausage, and broth. Bring to a boil. Reduce heat and simmer 25 minutes.
Ladle into bowls. Season with salt and pepper. For a thicker consistency, smash some of the potatoes with the ladle prior to serving.
