Bring the stock to a gentle boil (ensure the stock is flavorful, but not too salty). If using dried mushrooms, wash them well under tap water and then soak them for 5-10 minutes in lukewarm water to rehydrate them. Let any grit sediment settle to the bottom, pick up the mushrooms leaving the dirty water in the bowl. In a second pan, sauté the onion in 2/3 of the butter until soft and translucent. Add the rice and stir at medium heat for a couple of minutes (this will "toast" the rice, adding flavor). Add the wine and set the timer: 18 minutes if using Carnaroli, 15 minutes if using Arborio. Add the re-hydrated or fresh mushrooms. Keep stirring. When the rice dries out a bit, add some stock and go back to stirring. (Note: it might be necessary to lower the temperature, but make sure the rice keeps boiling, and so does the stock.) 3-4 minutes from being ready, add the saffron (dissolved in a tablespoon of stock). When the time is up, turn off the heat, move the pan off the burner and add the remaining butter. Keep stirring for 1 additional minute. At this point the Risotto should be creamy and soft, and without any liquid running around. Serve in bowls covered with the grated Parmigiano, some ground black pepper and (optionally) garnished with fresh thin-sliced green onion or chives. Eat immediately, as this dish absolutely can't be reheated.