In large saucepan over medium heat, crumble and cook sausage, potatoes, carrot, and onion until sausage is brown and vegetables are softened, about 8-10 minutes.

Sprinkle flour into pan. Cook, stirring frequently, 1 - 2 minutes.

Gradually stir in broth and milk. Cook, stirring occasionally, until soup comes to a boil.

Reduce heat to low and simmer for 10 minutes or until potatoes are tender.

Remove from heat and gradually stir in cheese. Stir until cheese is melted and smooth.