Like a noob, it took me a few good hours to figure this out. As far as I understand, you need to start a new project with laravel new <project> in directory 777. Thus, you would like:
run laravel installer laravel new web-project
The last bit in which you move the directory is optional, and you can leave it there or transfer it to any place where vhost can be configured.
Personal note: I really hoped the new Laravel application would be easier than that. I'm sure, however, with practice it will be easier :)
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