The heater circuit in the upstream O2 sensor is failing. That means when the computer switches to using the sensor data, the sensor hasn't heated fully, and isn't supplying accurate data to the computer causing it to run rich. Once the engine has run for a short while longer the exhaust gases heat the sensor past the point where it starts supplying accurate data and the engine runs smoothly till the next cold start.
Pop the hood and go the the manifold side of the engine. The sensor is in the exhaust pipe just below where it bolts to the exhaust manifold. Follow the wire up to the rear of the inlet manifold where you will find the plug. Disconnect the plug. The computer will light the check engine light because the sensor is disconnected, but the engine will run smoothly with no stutter from cold starts. Plugging the sensor back in will cause the stutter to reappear.
Fitting a new upstream O2 sensor is the cure.
