Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add cauliflower; cover and steam until tender, 5 to 7 minutes. Cool to room temperature.
Blend cauliflower, mushrooms, and green onions in a blender under chopped, yet still chunky.
Separate egg yolks and egg whites into 2 separate bowls. Beat egg whites in a bowl using an electric mixer until medium peaks form.
Combine half-and-half, butter, and flour together in a saucepan over low heat; cook and stir until white sauce is thickened, about 5 minutes. Cool slightly.
Stir white sauce, Parmesan cheese, cauliflower mixture, egg yolks, turmeric, salt, pepper, and curry powder together in a bowl; gently fold in egg whites using a spatula or wide knife. Pour egg mixture into a glass baking dish. Sprinkle paprika over egg mixture.
Bake in the preheated oven until golden brown and set in the middle, 30 to 35 minutes.
