Finely chop the onion; thinly slice the mushrooms; mince the garlic.
Mix the stock in a saucepan and heat it over a low heat to boiling point. Turn down the heat and leave to simmer gently.
Melt the butter in a heavy based pan, then gently sauté the onion until soft. Add the mushrooms and garlic and cook for 5 minutes until the mushrooms are tender.
Add the rice and stir for a minute until the edges are becoming translucent. Pour in the wine and let it bubble for a minute or so until absorbed. Then start adding the hot stock, one ladleful at a time, stirring until the stock gets absorbed before adding the next one.
When you have about a third of the stock left, add the chestnuts and keep adding stock and stirring. When you almost used up the stock, taste the rice. It’s ready when the sauce is thick & creamy, but the rice is still al dente (still has a bite). Keep stirring until it’s ready, then turn off the heat, add 3 Tbsps of the Parmesan and rest, under cover, for 5 minutes.
Serve with the remaining Parmesan and plenty of freshly ground pepper on top.