Cook sausage in a skillet over medium heat until heated through, 3 to 5 minutes. Transfer sausage to a plate.
Place onion, mushrooms, garlic, and Italian seasoning into the skillet over medium heat; cook until soft, about 5 minutes. Stir in pumpkin puree. Add vegetable broth. Reduce heat and simmer until flavors are blended, 20 to 25 minutes.
Stir in sausage, light cream, Parmesan cheese, and hot sauce; simmer 10 to 15 minutes more.