Sounds like you may have an injector or two that don't like being cold. If one hangs open, the HPOP may not be able to keep up with the HP oil demand to run the rest of the injectors, causing the rough running.
First thing to try is an oil change. These things are sensitive to oil condition.
If that doesn't help, get someone to pull codes, and you might also consider taking it to someone who could check the cylinder contribution when cold, using a scan tool that can display the PERDEL for each cylinder. Or you could pull the valve covers, and take a look at the oil coming out of the injector spouts when it runs cold. If one dumps more than the others, or doesn't dump any at all, that would be your suspect injector.
Good luck
First thing to try is an oil change. These things are sensitive to oil condition.
If that doesn't help, get someone to pull codes, and you might also consider taking it to someone who could check the cylinder contribution when cold, using a scan tool that can display the PERDEL for each cylinder. Or you could pull the valve covers, and take a look at the oil coming out of the injector spouts when it runs cold. If one dumps more than the others, or doesn't dump any at all, that would be your suspect injector.
Good luck