Restart stalling on '99 Accord ULEV-4

Hi, bought my son a used '99 Accord ULEV 4 cylinder automatic with
about 116K miles on it earlier this year. Car has been fine in all
regards. Except one:

If the car is fully warmed up, and you shut it off - then restart it
within approximately 10 minutes, it will start fine, then it runs for
about 5 seconds, then it stalls.

For example, if you stop to get fuel. Start it back up, it revs...runs
at idle for about 5 seconds, then stalls. If you feather the throttle
immediately after starting it, you can get it to stay alive.

My son also tells me that if he revs the engine in neutral, as it comes
down it will "bounce" to a very low RPM, start to stutter as if it will
stall, then it "catches" and idles okay.

What should I look at first?

Thanks,
Randy