Be careful you don't end up with two vapour barriers. If you foam inside make sure the sheathing outside can breathe and vice versa. the point of failure is when moisture gets trapped. hence the gap for the hardy board.
My camp build 2012 | Off grid tips, cartoons, paths taken
is my camp build where I used what is now called the cool roof on my washroom. the diagrams (of the highest technical specification, snort) are about 1/2 way down the page.
in 2012 it was a pretty new idea. but i used the ridge vent and 1" foil covered polyiso sheathing. 2013 was a record hot summer for us. and even tho 1/2 the roof faces due south the washroom never reached more than 1 degree above ambient. which. if you've ever been in a tin clad building on a hot sunny day ... you know is pretty amazing.
if you want solar powered cooling it is an excellent technique to use.
google buildingscience "perfect wall". they have done some excellent research in this area.