Quite unlikely, but if it's nothing electrical it may be worth looking for. Maybe the fuel shut off valve in the carb is faulty, letting in fuel even when the float bowl is full. It would seem fine when using good amounts of fuel (ie, moving) but when idling it would spill over and stall. The fuel in the cylinders will give you super-duper compression, making it hard to turn over. give it a few minutes, and it'll have dispersed (maybe into your oil..) and all is good.
As I say, unlikely, but worth looking into.
I'd give all the connections from the battery to the starter/gearbox (earth strap) a good shine up, and see if that helps it. If that does then you still have an idling problem but that could just be adjustment or a bit-o-crap in the idle jet.