The Tower Tops for Once Upon A Mattress.

Well, these aren't really flats per-se'. But the method is the same. You will need to make a curved inner structure and then cover that with strips of wood forming ribs. This all will get covered with whatever covering you wish to use.

xx1.jpg
Here we're using cardboard. We chose cardboard because it would add to the desired wood shingle look we were trying to achieve. Using muslin would have been a lot easier as the cloth would have formed well to the shape of the framing. The cardboard didn't want to take the curved shape and kept popping the staples. We had to switch to the longest staples we could find.
 xx2.jpg
 To get the smoothest surface possible will require using more ribs. Each rib will, most likely, show through the covering.  xx3.jpg