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 very tender, about 5 minutes.
Transfer cauliflower to a bowl and mash with a potato masher until few chunks remain; add 1/2 cup Cheddar cheese, sour cream, cream cheese, and Parmesan cheese and mix thoroughly. Spread the mixture into a 8-inch square casserole dish; top with remaining Cheddar cheese. Cover dish with aluminum foil or lid.
Bake in preheated oven until hot and bubbling, 20 to 25 minutes. Remove cover and continue baking until the top is browned, about 10 minutes more.
