Put the pasta into a large pot of lightly salted boiling water and cook until al dente- usually a minute or two less than it says on the packet. Preheat the oven to 190 C, 375 F, Gas Mark 5.
Meanwhile slice the mushrooms quite thickly and saute them in the olive oil over a fairly high heat until golden brown. You may need to do this in batches. The mushrooms will throw out a lot of water and you have to drive this off, or you will end up with a grey liquid when the dish is baked.
Add the butter to the mushrooms together with the garlic, chestnuts and seasoning. Drain the pasta and add to the mushrooms, then pour in the cream. Grate in a generous amount of nutmeg then bring to the boil. Check seasoning.
Transfer immediately to a gratin dish and sprinkle over the cheese. Put into the preheated oven and bake for 45 minutes, until the cream has reduced and it is golden and bubbling.