First, preheat your oven to 400ºF because you need to roast the squash. Take the squash and slice it in two laterally. Scoop out and discard the seeds, and then rub the squash with a tablespoon of olive oil. Put it on a roasting pan and roast for 30 to 45 minutes. It is done when the top turns light brown and it is all soft and mushy. Once done, scoop out the cooked squash, mash it up a bit, and put it in a bowl until you need it.
Dice the shallot and clean the mushrooms. Discard the tough stems.. Then, slice the mushrooms.
In a 2 quart pot, bring the stock to a simmer.
Now, in a different 4 quart pot, on medium heat, add 1 tablespoon of butter and oil. When it is good and hot, add the shallots. After a minute, add the mushrooms and thyme and cook for another 2 minutes. Then, add the rice, salt, and pepper, and stir for 1 minute.
Next, add the white wine and continue to stir, until it is almost evaporated. At that point, add enough boiling stock to cover the rice completely. Then, add the cooked squash. Keep the heat at a level so the liquid burbles briskly, but not too vigorously. Stir every minute or so and whenever the liquid drops below the rice, add more stock. If you run out of stock, start using boiling water instead. After about 15 to 20 minutes, the risotto should be done.
To finish, remove from heat, adding the remaining tablespoon of butter.