Is the parking brake engaged? Does it do it with the engine off? I hear that clanking (if that's the sound you're referring to) sound when the car is off and parked for short period of time.
Parking brake is engaged. Engine is running. It is not a creak that sometimes emanates from braking systems. This is very dynamic.
I'll isolate the location as best I can. Something is slamming shut, definitely metallic. Almost sounded as if it was from the throttle body, which would be very odd.
Mine does that when you shut it off haven't really thought much of it. My driver's side exhaust solenoid if leaking so it need to go in anyways I'll have them look at that also. Just adding that mines more of a clunk than a metallic sound but I haven't listened to it with the hood open.
It's not fast enough to be something rotating internally. Almost sounds like air escaping from a blow off valve.
Some guys experienced a pop from the intake on shut off intermittently from air pressure. My car did it when I unplugged the throttle position sensor during a part install. Took a few drive cycles for it to relearn itself. I think you have something loose or the throttle body is learning itself.
Are you in a cold climate or high elevation? Check all your sensors to be sure they are attached and see if the noise is originating from the throttle body. I would almost bet my lunch that is where it's coming from
Listen to about 13:25 on, specifically around 13:28. There's a sound that I think sounds similar to that that you can hear. Could it be the CMCV's sticking? I believe the 350 IM has them.