Heat 3 tablespoons of the olive oil in a very large skillet over medium-high heat. Add the mushrooms; season them generously with salt, pepper, and cook, making sure not to move around too much, until the mushrooms release their water, 5-6 minutes. Remove the mushrooms and set aside in a plate. In the same skillet heat two more tablespoons of the oil, add the garlic and cook 1 minute. Add the sausage and sauté for 4-5 minutes until crispy and golden. Add the reserved mushrooms to the sausage, toss gently, cover and keep warm. Bring a large pot of salted water to a boil. Heat gently the pumpkin puree and season with 1 tablespoon of the oil, salt and pepper to taste. Cook the Fettuccine according to package directions and drain, reserving 1/2 cup of the pasta cooking water. Transfer the Fettuccine to the pan.
Loosen the pumpkin puree with a little of the pasta cooking water if needed and spread it on the plates.
Divide Fettuccine among plates and serve.