Laravel 5.1 How to Log - PHP Fatal error: Allowed memory size of X bytes exhausted

I am having this random out of memory issue in my production for specific api's calls. Laravel log has nothing logged. I am not able to figure out for what parameters it is going out of memory.

Is there a way to setup register_shutdown_function and put it in Laravel somewhere, where in I can put the stack trace in the log. Or any other way to log the error and stack trace for the same?

via Chebli Mohamed