Rose Blush: That must have been a really hot fire over relatively thin soil. I have been interested in fire regimes for some time, and how slash and burn horticulture works. I never finished with the research, but I did find that in slash and burn there is a rotation of burning among a designated group of fields. It takes 12 to 15 years after a field is burned before it can be farmed. And old fields have advanced to the development of trees and those are the one's that will be in line to be burned. The trees provide biomass and ash that improve the fertility of the fields. But most slash and burn farm regimes are in the tropics. And of course few governments have ever taken the trouble to learn how they work--they only want to kill slash and burn because it encroaches on land they want for development. It only seems wasteful to them, and slash and burn mostly has a bad (undeserved) reputation.
But I wonder if there are not some type of grasses that could be planted on your burned area in a dry climate to start a cycle of plant life.