2003 Jetta GLI Hot Start issues

Hey guys. I’ve got a 2003 Manual 2.8l VR6 Jetta.

It starts and runs fine when cold all the time, and it’s a great car. However, if I turn it off after driving it for more than a few minutes and try to crank it, it starts but wants to die. I have to give it gas, put it in a gear, move forward for a few seconds, and it’s fine.

Just that first idle on a hot start is hard to keep it alive. If I let it die, it floods the engine. I have a code P1117 which I believe can be for a few different things, but I replaced the oxygen sensor after the cat and it didn’t affect it. I’m putting new coils on it today just to do it, and I’ll update if that helps.

What do you guys think? Could it be the ECT sensor? I did also have a code for evap leak detection pump shorted, but I don’t think it’s related.