I would use a for loop instead of recursive calls:

protected function _hashPassword($password = NULL, $rounds = 1000) {
    if (!isset($password)) throw new Exception('No password set!');

    $salt   = 'K^^%/m>(|{z= $1^>%>W[=4U5*p|,E';
    $pepper = '08[)^,&%^^771^=>&,E[XP::4})h*I';

    $dinner = $salt . $password . $pepper;

    for ($i = 0; $i < $rounds; $i++) {
        $dinner = sha1($dinner . $password);
    }
    return $dinner;
}

Furthermore, I would use the username as 'pepper'.

I would use a for loop instead of recursive calls:

protected function _hashPassword($password = NULL, $rounds = 1000) {
    if (!isset($password)) throw new Exception('No password set!');

    $salt   = 'K^^%/m>(|{z= $1^>%>W[=4U5*p|,E';
    $pepper = '08[)^,&%^^771^=>&,E[XP::4})h*I';

    $dinner = $salt . $password . $pepper;

    for ($i = 0; $i < $rounds; $i++) {
        $dinner = sha1($dinner . $password);
    }
    return $dinner;
}

From http://php.net/manual/en/functions.user-defined.php:

It is possible to call recursive functions in PHP. However avoid recursive function/method calls with over 100-200 recursion levels as it can smash the stack and cause a termination of the current script.

Furthermore, I would use the username as 'pepper'. It would make your hash more unpredictable.