Install PHPStorm 2017.X
Install Xdebug helper for chrome
Via ssh (choose a tool like putty, WinSCP, MobaXterm etc.) Install xdebug, in your case laravel gets Ubuntu 16.04 by default with Nginx so we need to follow these instructions The values I used are
; Enable xdebug extension module zend_extension=/usr/lib64/php/modules/xdebug.so xdebug.remote_enable=1 xdebug.remote_handler=dbgp xdebug.remote_port=9000 xdebug.remote_autostart=1 xdebug.remote_connect_back=1 xdebug.remote_host=10.0.2.2
But note that I use my own vagrant installation (homestead is based on Vagrant) with CentOS and apache instead. Restart your virtual machine after config changes.
vagrant / homestead halt
and start again
vagrant / homestead up
Config Xdebug helper extension in chrome by right clicking the symbol > options and set your IDE key to PHPStorm in the dropdown menu.
Configure PHPStorm, like a lot
hint: Settings has the shortcut ctrl + alt + s
Check the following settings. Don't forget to add both http and https in the Servers Setting and most important, don't read over the path mappings part.
And last but not least click these buttons, the first button with the phone horn actually has reversed icons in my opinion: when debugging it should have the little green part, altough logically red would mean stop, now it means start.
button 2 starts your url with a session var in the query string!
P.s. from your question: I think you need to go 1 level up root of laravel instead of public folders
edit: I just installed homestead at home and it comes with xdebug installed: