I beleive the exhuast port is split between what's coming out of the combustion chamber (both valves), and fresh air from the air injection to supply oxygen to help the catalytic converter burn any remaining unburnt fuel.
In your picture, the right side should be what's coming from the combustion chamber. As for your actual question about the build up around the vertical shaft (stem?) in the left side, I don't recall seeing any of that when I've had my header off (though it's been awhile).
It does look like carbon buildup, but there shouldn't be any exhaust gas exiting there. It's possible that gas fumes build up in the airbox, from slow speed stop and go driving, then get sucked into the air injection and passed to those ports. Since it would be raw fuel, it might be collecting there, as the narrowest point in it's travel with the highest temperature, and building up as tar / gum.
Can't be sure, but it's the only theory I have for you at the moment. Hope i