• Freshly ground black pepper
Generously butter a 2-quart shallow ceramic or glass baking dish. Put oven rack in middle position and preheat oven to 425 degrees. Melt 3 tablespoons butter in a 2-quart heavy saucepan over moderate heat until foam subsides, then add flour and make a roux, whisking while cooking, 2 minutes. Add milk in a slow stream and boil, whisking, then reduce heat and simmer, whisking occasionally, until thickened, about 3 minutes. Whisk in squash purée, cheese, brown sugar, salt, cayenne and nutmeg until combined (mixture may not be completely smooth), then transfer to a large bowl and whisk in egg yolks.
Beat whites with a pinch of salt in another bowl with an electric mixer until they just hold stiff peaks. Fold one-fourth of whites into squash mixture to lighten, then fold in remaining whites gently but thoroughly. Spoon into baking dish and bake, uncovered, 15 minutes. Loosely cover top with foil and bake until puffed, golden brown, and just set, 25 to 30 minutes. Serve immediately, with freshly ground pepper.
Nutrition information per serving: