Start by slicing your sausage into circles or half circles. Prepare the vegetables by peeling and cubing potatoes, dicing onion, and peeling and cutting carrots into circles.
In a soup pot, add the sausage and lightly brown over medium heat. Retain about 2 tablespoons of grease from sausage (drain or add cooking oil as needed).
To the same pot, add in carrots and onion. Season with salt and pepper. Cook for a few minutes, or until onions are starting to soften.
(optional) Sprinkle flour over sausage and vegetables. Stir continuously for a few minutes until flour is starting to turn light brown.
Pour broth into pot, stirring as you do. Add potatoes and ensure the broth covers them.
Bring to a boil, then reduce heat to simmer. Allow to cook until carrots and potatoes are soft, about 20 minutes.
(optional) To create a creamy soup, you'll need to blend some of the potatoes and broth together. Do this by using an immersion blender, or by blending about 3 cups of potatoes and broth in a regular blender.