How to Make It
Preheat oven to 400°F with oven rack in lowest third of oven. Generously butter a 2-quart soufflé or baking dish and coat with ¼ cup Parmesan.
Melt butter in medium saucepan over medium heat. Add shallot and mushrooms and cook, stirring often, until mushrooms begin to soften, about 5 minutes. Add flour and cook, stirring with a wooden spoon, until nutty smelling, about 3 minutes. Gradually whisk in milk in 4 additions. Bring to a gentle simmer and cook, whisking often, until thickened and mixture coats a spoon, 4 to 5 minutes. Remove from heat and stir in the spinach, ½ teaspoon kosher salt, several grinds black pepper, a pinch of nutmeg, and gruyere. Whisk in the egg yolks.
Beat egg whites with an electric mixer on low speed. When they begin to foam, increase speed to high and beat until stiff peaks form, about 3 minutes. Gently fold ¼ of the whites into mushroom mixture, then fold mixture into remaining whites. Quickly transfer to prepared dish and top with remaining ¼ cup Parmesan.
Transfer to oven on lower rack and immediately reduce temperature to 375°F. Bake until puffed and golden, 25 to 30 minutes.