2005 Ford 500 rough start

My 2005 Ford 500 has a rough starting issue. The first start in the morning it starts right up no issues but the other day i drove it around the block, pulled into the driveway, turned the car off, ran inside quick then attempted to start the car again and it ran real rough like it was starving for gas. At one point that day it cranked but wouldn’t start at all so I let it sit over night and started it in the morning. Started right up so after 15 seconds or so i turned it off and tried to start again and it runs rough after that like its starving for gas but quickly recovers and runs fine. Now everytime I start it it cranks fine first thing but once I turn it off and attempt yup restart it runs rough for 10 seconds or sip until it catches up and smooths out.

I replaced the fuel filter, added dry gas, no check engine light, fuel pressure is between 46-50 at start up and 40 psi running. It has 125,000 miles. It was suggested to clean throttle body but does anyone have any ideas? What kills me is no check,engine light or hidden codes on the reader. Any ideas would help.