Heat the olive oil in a large dutch oven or stock pot over medium/high heat.
Add the sausage and cook until browned. Using a slotted spoon, transfer the cooked sausage to a bowl. Pour off all but 2 tablespoons fat. Return the pot to the heat.
Add the onion and carrots to the pot cooking until softened, approximately 3-4 minutes.
Stir in the garlic and cook for 1 minute. Add the Italian seasoning and tomato paste, stirring to combine. Continue cooking for 2-3 minutes longer or until the tomato paste begins to turn a deep burgundy color.
Add the wine to the pot and using a wooden spoon, scrape up the brown bits on the bottom of the pot. Bring to a boil and cook until reduced by half.
Add the tomatoes, cooked sausage and beef stock to the pot stirring to combine. Bring the soup to a boil, then reduce the heat to low.
Stir in the potatoes and cook for 10-15 minutes or until tender.
Slowly stir in the half and half and cheese. Simmer for an additional 1-2 minutes then season with salt and pepper to taste.
Serve immediately with extra parmesan cheese, if desired.
Notes
Leftover Sausage Potato Soup can be stored in an airtight container refrigerated for up to 5 days.