Laravel version 5.6.10 and later has support for a permission element in the configuration (config/logging.php) for the single and the daily driver:
'daily' => [
'driver' => 'daily',
'path' => storage_path('logs/laravel.log'),
'level' => 'debug',
'days' => 7,
'permission' => 0664,
],
No need to juggle with Monolog in the bootstrap script.
Specifically, support was added in https://github.com/laravel/framework/commit/4d31633dca9594c9121afbbaa0190210de28fed8.