I'm not sure whether there is a 'best' way to do it.
Personally I've had to do this twice and both times I've started from scratch. With the old project, you have an overview of the end product. You have your classes, your routes, your database structure all worked out.
From there, it's just a matter of porting it over to the Laravel way, which is (I think) easier than trying to copy/paste code.