Heat up a dry frying pan over a medium heat. Add the mushrooms and dry fry for 4 to 5 minutes, making sure they don't burn. Once the mushrooms have gotten rid of some of their water; add butter and raise heat. Fry intensely until they get crispy. Salt generously.
Peel and finely chop butternut squash while the mushrooms cook. Remove the mushrooms from the pan, and then cook the butternut squash in oil or butter on medium-high heat until they are soft.
Chop onion into small pieces and add onion and minced garlic to the butternut squash. Cook until translucent.
Add salt and pepper, then add the mushrooms back. Then add cream, cayenne pepper and parsley. Lower heat to low and let simmer for 5 minutes. Add salt and pepper to taste (if needed).
Bring a saucepan of water to the boil over a high heat and cook the tagliatelle according to the instructions on the packet, until al dente. Drain and toss with the sauce; serve immediately.