Bring a large pot of water to a boil.
Meanwhile, heat a deep skillet over med-high heat; add in olive oil and sausage.
Brown the sausage and crumble it with a wooden spoon.
Move the sausage to one side of the pan; add in the mushrooms, garlic, and onion to the other side of the pan.
Cook until the mushrooms brown, then season with salt and pepper.
Combine the sausage and veggies; deglaze the pan with the wine.
Add in the chicken stock; heat for 1 minute.
Stir in the pumpkin; it will be thick; stir in the cream, sage, nutmeg, and cinnamon; adjust seasoning with salt and pepper; reduce heat to low.
Add salt and pasta to the boiling water; cook until al dente.
Drain the pasta well and add it to the pumpkin mixture; top with cheese and chives.