Melt the butter in a large saucepan over medium heat. Add the mushrooms and cook, stirring often until the mushrooms are browned and most of the liquid has evaporated, about 5 to 7 minutes.
Add the onions and garlic to the pan and saute until soft and translucent, 3 to 4 minutes.
Add the flour and cook, stirring with a wooden spoon, to make a light roux, about 2 minutes. Whisking constantly, slowly add the milk and continue to cook, stirring occasionally until thickened, 5 minutes.
Add the salt, pepper, nutmeg, spinach and 1 1/2 cups of the Parmesan and cook, stirring, until thickened, about 2 minutes.