Bring a large pan of salted water to the boil and cook the pasta according to the packet instructions until just tender. Reserve 150ml of the pasta water, then drain.
Meanwhile, heat the olive oil and butter in a large frying pan over a medium-high heat. Add the mushrooms in a single layer and cook for 6 to 8 minutes, without stirring too often, until golden.
Add the garlic and thyme and cook for 1 minute, until fragrant.
Pour in the double cream and simmer gently for 2 to 3 minutes, until slightly thickened.
Stir in the Parmesan until melted, then season with salt and plenty of black pepper. Loosen the sauce with a splash of the reserved pasta water if needed.
Add the drained pasta to the pan and toss well so every strand is coated. Serve at once, topped with extra Parmesan and parsley.