Laravel - How to register a new user using the AuthController that Laravel provides in another controller

So I am building a checkout functionality. If the user is a guest he could use his credentials to make a new registration with the order he makes. I have used the auth scaffold Laravel provides with the command php artisan make:auth. I have an OrdersController and the AuthController that comes with the framework. How can I register a new user within my OrdersController? Here is my code: checkout.blade.php:

<li class="col-md-12 col-sm-12">
    <h4>Register</h4>

    <input id="create-act" type="checkbox" class="input-chkbox" name="register">
    <label for="create-act">Create user account?</label>
</li>
<li class="col-md-12 col-sm-12 create-account">

    <label for="password">Password<em>*</em></label>
    <input required type="text" class="input-text" id="password"
           name="password">
</li>
<li class="col-md-12 col-sm-12 create-account">
    <label for="password_confirmation">Confirm Password<em>*</em></label>
    <input required type="text" class="input-text"
           id="password_confirmation"
           name="password_confirmation">
</li>

OrdersController inside addOrder method:

if(isset($_POST['register'])) {
 $this->validate($request, [
        'password' => 'required|password',
        'confirm_password' => 'required|'
    ]);
}

I want to register the new user inside this if. How can I do that?

Edit: Here is my protected function create inside my AuthController.

protected function create(array $data)
{
    $confirmationCode = str_random(30);

    $user = User::create([
        'name' => $data['name'],
        'email' => $data['email'],
        'password' => bcrypt($data['password']),
        'confirmation_code' => $confirmationCode
    ]);

    $user->roles()->attach(Role::where('name', 'Customer')->first());
    $cart = new Cart();
    $cart->user_id = $user->id;
    $cart->save();
    if(Session::has('cartItems')) {
        foreach (Session::get('cartItems') as $sessionCartItem) {
            $cartItem = new CartItem();
            $cartItem->product_id = $sessionCartItem['product']->id;
            $cartItem->cart_id = $cart->id;
            $cartItem->size = $sessionCartItem['size'];
            $cartItem->quantity = $sessionCartItem['quantity'];
            $cartItem->save();
        }
    }

    Session::flush();
    $cart->save();

    $email = $user['email'];
    $name = $user['name'];

    Mail::send('auth.emails.user-confirmation', ['name' => $name, 'confirmation_code' => $user['confirmation_code']], function ($message) use ($email, $name) {
        $message->from('[email protected]', 'Name Family')->to($email, $name)->subject('Confirm email');
    });

    return $user;
}