2. Meanwhile, heat the chicken broth in a saucepan and keep hot over low heat.
3. Heat the olive oil over medium heat in a separate, medium-sized pot. Add the onion and cook until it turns translucent, about 5 minutes. Season lightly with salt and pepper. Add the mushrooms and cook until the mushrooms become tender, about 8 minutes. Add the garlic and thyme and cook 2 minutes more.
4. Add the rice to the onion mixture, stir and turn the heat to low. Add about 1 cup of the hot stock to the rice mixture, and stir slowly until the stock is absorbed.
5. Continue to add the stock 1 cup at a time, stirring slowly, letting the rice absorb the stock before adding more.
6. The risotto is cooked when it is creamy on the outside and slightly firm (al dente) in the center, about 20 to 25 minutes in all. Stir in half of the Parmesan cheese. Gently stir in the squash chunks just to reheat without crushing. Remove from the heat. Season with salt and pepper to taste. If the risotto is too thick, add a little more stock until it becomes creamy.
7. Divide the risotto into serving dishes, sprinkle with the remaining cheese and serve immediately.