Multiple session cookies created for the same Laravel app

I have a Laravel 5.2 app laying on a domain like this: https://www.example.com.

The laravel_session cookie is configured to use the dot notation (to include subdomains):

config/session.php:

'cookie' => 'laravel_session',
'path' => '/',
'domain' => env('SESSION_COOKIE_DOMAIN', null)

.env file on the server:

SESSION_COOKIE_DOMAIN=.example.com

I'm using the database as the session driver.

Now, there are cases when the session cookie gets duplicated, and in the cookie list I can see entries like these:

• laravel_session, domain: .example.com
• laravel_session, domain: .www.example.com

The same thing happens with the Facebook session cookies, when a user used Facebook to authenticate:

• fbm_123456, domain: .example.com
• fbm_123456, domain: .www.example.com

In both cases, the expiry dates on the duplicated cookies are different

This cookie duplication causes problems with authentication - some users try to log in, but get redirected back to the homepage, with the auth state unchanged.

I can't seem to reproduce the issue, or rather what's causing it. I think, though, it may be linked to Laravel session expiring, or to logging the user in via the remember-me token.

Does anyone have an idea why would the cookies be duplicated?

UPDATE:

Actually, I realize now that the only difference between our other Laravel project and this one is that here we explicitly set the laravel_session domain (to .example.com). May be a lead.