Heat the oven to 400° and coat an 11- by 7-inch pan or 1 1/2-quart baking dish with cooking spray. Heat the oil in a large skillet over medium heat. Add the squash, reduce the heat to medium-low, cover, and cook for 10 minutes. Stir in the onion and apples. Cover the pan again and cook five more minutes. Transfer the mixture to the prepared baking dish. Add the thyme, salt, and pepper and toss gently to combine.
To make the topping, stir together the bread crumbs and butter in a medium bowl. Stir in the Parmesan until evenly blended. Sprinkle the topping mixture evenly over the squash mixture and bake until the crumbs are golden brown, about 20 to 30 minutes. Serve immediately.