Pull the plugs and have a look at them.  it could be that one or more
of the plugs  is getting oil fouled...  Then when you restart the car,  
you have none of the advantages and a cold start (ie moree fuel and
higher idle speed), so you are noticing the engine misfiring.  Once the
plug heats up enough to start firing properly, it runs smoothly again.

Just a theory, but a relatively simple one to test.

Marty

This is nothing more than a stab at your car's problem, especially since
it's a gray market vehicle.

I suspect the engine's control computer is misreading either the
engine's temperature or the O2 in the exhaust or throttle position but,
as I wrote, its only a stab at the problem. This problem is engine
control related, not just a simple vacuum leak.

It's OK if you start it cold and drive continuously for a long distance
but NOT if you stop for gas etc. and then restart it.

This won't be easily found. If the engine is not hot BUT the computer
believes it IS hot then a lean air/ fuel ratio will be put into the
engine. A faulty temperature sensor might be the cause. Or a bad O2 sensor.

The throttle position sensor is less of a suspect as the problem only
occurs during warm up.

You won't solve this so find a shop that understands the difference(s)
between the USA spec and gray market spec cars.