i have this exact same thing happening for the last week.
cold morning start, kick it over, save it with a touch of the pedal and everything's perfect. or let it stall and kick it over again, no pedal, idles perfect. any other time after the first start of the day is perfect.
i thought it might be the check valve in the pump not holding pressure in the fuel rail. so i tried priming it 3 times instead of once before the cold start. but it made no difference.
so i'm guessing its not a fuel issue. i'm upgrading my fuel pump soon anyway, but dont think it will sove this problem.
I will have to eventually clean out the two valves mentioned above. I was trying my best to avoid that