Melt 15 g (½ oz) of the butter in a large saucepan and fry the mushrooms for about 5 minutes until lightly browned. Lift out with a slotted spoon on to a plate and set aside.
Season the rabbit lightly with salt and pepper. Melt another 25 g (1 oz) of the butter in the pan and fry the rabbit for 5 minutes, until beginning to colour. Add the onion and celery and fry gently, stirring frequently, for about 5 minutes until the vegetables have softened.
Stir in the garlic, thyme and rice and cook, stirring, for 1 minute. Add the wine and cook quickly until the wine has been absorbed. Gradually add the hot stock to the pan, a ladleful at a time, and cook, stirring frequently, until each ladleful has mostly been absorbed before adding the next. This should take 20–25 minutes, by which time the rice should be tender but retaining a little bite and the consistency should be creamy. You may not need all the stock.
Return the mushrooms to the pan and stir in the remaining butter and the parsley. Season to taste with salt and pepper and serve immediately.