One thing that comes to mind is a "leaky fuel injector". When this occurs, after driving and shut off, a small amount of fuel will leak past the injector into the cylinder. When the engine is restarted, it can take a few seconds for the engine to burn off the extra fuel (rich for a bit) so you can have a rough idle for a few seconds until that cylinder cleans up and the proper fuel is again being delivered.
How many miles are on your engine? Any check engine light?
How many miles are on your engine? Any check engine light?