Engine stalling after be driven hard?

I was going to suggest a fuel issue as well
(maybe as simple as running the bowls dry, and not being able to replenish them quick enough) but the slow cranking doesn't make sense

do I read it right, to think it cranks at a lower RPM when this happens then under normal circumstances?
and if the engine is hot, and you shut it off and turn it back on, does it turn slow like when it stalls or fast like when its cold?