Heat olive oil in a large pot over medium-high heat, then add the mushrooms in a single layer. Let them brown without stirring too much so they caramelise nicely. Once golden and slightly reduced, season lightly with salt and pepper and set aside.
Add a bit more oil if the pot looks dry, then add the sausage meat. Break it apart with your spoon and cook until browned and slightly crispy. Stir in the garlic and sauté for about 30 seconds. Pour in the white wine and let it reduce until most of the liquid evaporates, scraping up any browned bits for extra flavor.
Pour in the chicken stock and heavy cream, then stir in the uncooked pasta and return the mushrooms to the pot. Let everything simmer gently until the pasta becomes al dente and the sauce thickens. Add extra stock or water if needed. Turn off the heat and stir in Parmesan, parsley, and spinach until the greens wilt. Taste and adjust seasoning.