Why does the engine cut out?

What is your question?

Why is it when my gas tank is about half full the engine will cut out. It runs great and no check engine light no codes. It will usually start right up after a few times have to let it sit for 10 to 15 min. And no issues after.

What makes this problem better or worse?

Only seems to happen at half tank of gas

How long has your 2001 Hyundai Elantra had this problem?

A couple months