In a Dutch oven, saute onion and carrots in butter till onion is tender. Add potatoes and broth. Bring to a boil. Reduce heat; simmer till vegetables are tender, about 25 minutes. Remove from heat. Puree at least half of mixture in blender (more blended makes creamier soup). Return to saucepan. Add milk and sausage. Cook over low heat till sausage is heated through.