I hearby declare the problem in my 318is to be FIXED. (Or to be now so minor that I'm going to choose to ignore the very minor nature of what's left)
Here are the symptoms I used to have:
Restarting the engine warm would result in the engine starting instantly and idling nicely, but then it would shortly result in a 30-60 second interval of missing, coughing and sometimes the engine would die.
I have found two causes for this issue:
1.) The ICV (Idle Control Valve) was backwards! There is an arrow cast into the body of the ICV. This arrow must point "down". (The flow must be away from the valve cover.)
2.) A defective TPS (Throttle Position Sensor). I replaced this sensor.
The result is that I can now start the engine warm without worrying about the car not going anywhere for 30-60 seconds. It still might hesitate for a second, but it goes away almost instantaneously. That's close enough for me.
I hope this fixes everyone else's issue.