A mate of mine sent me the link to quite a cool video on the web about studio lighting. One of the lights this guy used was a beauty light. He explained the principles of this
device so well I thought I can do that.
Simply put a beauty dish is a reflector that prevents the light from the flash directly hitting the subject. All of the light is diverted to the outsides of the reflector and back to the subject off the rim. Here is version 1.0 and it works great. Cost 0$ 
Construction
Take a bowl, white or silver cut a whole for the flash to peer through. This is the reflector. Put a reflector over the hole where the flash peers through to prevent the flash shining on the subject (in this case an old hard drive platter – why… it was lying around) put a spacer between the two reflectors (in this case a bolt with nuts.
i like your idea for the dish but your self-portrait is not indicative of the shadow-less soft light that a traditional beauty dish produces.