The curl parameter "--user" just passes basic auth info in the HTTP request. You can easily use the BasicAuth middleware => http://laravel.com/docs/5.0/authentication#http-basic-authentication

However I don't think this is the best approach. If you have several servers/services doing requests on your Laravel instance, you should at least use a seperate user for each one. Otherwise if one of your passwords get compromised you have to change credentials on all servers.

A better solution in my opinion would be to use an access (or authentication) token based mechansim or even better certificates (if there are critical data involved). But that really depends on what kind of data you process.