You can add cookies to the request to the given url:
Browsershot::url('https://example.com')
->useCookies(['Cookie-Key' => 'Cookie-Value'])
...
You can specify the domain to register cookies to, if necessary:
Browsershot::url('https://example.com')
->useCookies(['Cookie-Key' => 'Cookie-Value'], 'ui.example.com')
...