とりあえず動きますが、やっつけ感が否めないです。もっと綺麗に書けそうです。

app/Providers/AppServiceProvider.php

<?php

namespace App\Providers;

...

use Swift;
use Swift_DependencyContainer;
use Swift_Preferences;

class AppServiceProvider extends ServiceProvider
{
    ...

    public function register()
    {
        ...

        // ここを追加
        Swift::init(function () {
            Swift_DependencyContainer::getInstance()
                ->register('mime.qpheaderencoder')
                ->asAliasOf('mime.base64headerencoder');
            Swift_Preferences::getInstance()->setCharset('iso-2022-jp');
        });
    }
}

app/Mail/OrderShipped.php

<?php

namespace App\Mail;

...

use Swift_Mime_ContentEncoder_PlainContentEncoder;

class OrderShipped extends Mailable
{
    ...

    public function build()
    {
        return $this->from('example@example.jp')
                    ->subject('日本語サブジェクト')
                    ->text('emails.order_shipped')
                    ->withSwiftMessage(function ($message) {
                        $message->setCharset('iso-2022-jp')
                                ->setEncoder(new Swift_Mime_ContentEncoder_PlainContentEncoder('7bit'));
                    });
    }
}

参考

SwiftMailerでJIS(iso-2022-jp)のメールを送る件