Coat a 13 x 9 inch baking dish with nonstick cooking spray.
In a large skillet, heat the butter and oil together over medium high heat. When the butter is melted, add the onion and cook, stirring, until softened, about 3 minutes. Add the squash and cook another 3 minutes, stirring a few times. Stir in the spinach, salt, pepper, and nutmeg and cook, stirring, until the mixture begins to lose some of its moisture, about 5 minutes. Stir the flour into the squash mixture and cook until absorbed, another 2 minutes. Add the milk and Boursin and stir until the mixture comes to a boil and the cheese has melted. Transfer to the prepared dish. (At this point, you can let cool, cover, and refrigerate for up to 2 days. Bring to room temperature before continuing.).
Preheat the oven to 350 degrees F. Bake the casserole until the top is golden brown, about 20 minutes. Let rest 5 to 10 minutes before serving.