Cook the pasta in a pan of boiling salted water according to the package instructions, then drain, reserving a cupful of cooking water. Meanwhile, peel and finely slice the garlic. Place it in a large non-stick frying pan on a medium-high heat with ½ a tablespoon of olive oil, followed 1 minute later by the mushrooms, tearing up any larger ones. Season with sea salt and black pepper, and cook for 8 minutes, or until golden, tossing regularly.
Toss the drained pasta into the mushroom pan with a splash of reserved cooking water. Finely grate in most of the Parmesan, stir in the crème fraîche, taste, season to perfection, and dish up, finishing with a final grating of Parmesan.