Meanwhile, heat oil in a large saucepan over medium heat. Add shallots; cook, stirring, until fragrant, about 1 minute. Stir in squash and mushrooms; cook, stirring often, until the mushrooms give off their liquid, about 5 minutes. Add thyme, salt, pepper and saffron (if using); cook for 30 seconds. Add rice; stir until translucent, about 1 minute. Add wine (or vermouth) and cook, stirring, until almost absorbed by the rice, about 1 minute.