Try cooking naans on a preheated pizza stone.

In my experience, the only way to do this at home is to preheat a large (14 inch) cast iron skillet under the grill at its hottest, take the pan out and heat it some more on the  stove, dip the base of the Naan in water, place on the pan , prick it in several places the replace under the grill.It cooks as quickly as in a Tandoor, and can be as good.