A parabolic solar cooker is essentially a solar thermal collector [1] used to cook food or pasteurize water. Parabolic designs have been used for centuries. The idea to concentrate light using curved mirrors was developed by the Greeks, Aztecs, Incas, Romans and Chinese. The Incas used bronze and gold for their mirrors and they built structures that were several stories high. This technology seems to have appeared around the same time for each of the civilizations.
There are many designs and models for parabolic solar cookers. Some are made with locally gathered scrap materials while others are manufactured using highly machined, durable but more expensive materials. Here are links to and photos of a number of parabolic solar cooker designs.
http://www.appropedia.org/images/0/0f/Grilling_meat_with_parabolic_solar_cooker.jpg
http://solarcooking.org/plans/