Place a small saucepan over medium to high heat. Once heated, add a little olive oil, onion, garlic and thyme. Sauté for 2-3 minutes.
Add the rice and sauté for 2 more minutes.
Add the mushrooms and sauté for another 2 minutes.
Add the wine and, once the alcohol has evaporated, add salt and pepper and mix.
Add the water, in batches, and cook, stirring at regular intervals, until it is absorbed. Repeat this process until the mixture is completely thickened, as if making a risotto.
Remove from the heat and add the butter and Parmesan. Stir constantly so that it gets a nice creamy texture but, at the same time, not too wet to help form balls later.
Pour the mixture into a bowl and transfer to the refrigerator for 2 hours, until it cools and thickens well.
Wearing disposable gloves, form medium size balls and place them on a plate.