possible cause are the injectors. If they get older deposits can be formed at injector nozzles and the injectors can start to leak after you switch off the engine. Then you will get a fuel vapor problem in the injection lines causing the described hard start of the engine.
Try some chemical fuel additives e.g. Techron or Liqui Moly Injection Cleaner best together with an Italian tune-up.
If this will not help you can test the fuel system for internal leakage. The fuel pressure should not drop below 3.4bar after switching off the engine. Else you should renew your injectors.
Michael (86, 420SL)