Filter user list that meta_value is empty

I think the use of meta_query is in order:

$user_query = new WP_User_Query( 
    array( 
        'meta_query'=> array( 
            array( 
                 'key'=> 'birthday', 
                 'compare' => 'NOT EXISTS' 
            ) 
        ) 
     ) 
);

Basically, this looks for all users where the meta key of birthday doesn’t have a value ie doesn’t exist. More info about meta queries in WP_User_Query can be found here