How to render a fragment?

Question

OctoberCMS

In general, the essence is as follows, there is a basket, there is a button to add to basket. On the button weighs data-request = "onAddToCart"
Below is onAddToCart itself

public function onAddToCart(){
      $product = \vladimir\catalog\Models\Product::find( Input::get('id') );

      if (Input::get('qty') !== null){
        $qty = Input::get('qty');
      }

      $item = new \stdClass();
      $item->id = $product->id;
      $item->name = $product->name;
      $item->price = $product->price;
      $item->img = $product->images[0]->path;
      $item->qty = count($this->getItems());

      Session::push('cart', $item);

      return [
        '@.cart-items' => $this->renderPartial('@cart-item.htm', ['item' => $item]),
        '.total-price' => $this->renderPartial('@cart-price.htm', ['item' => $this->Total()]),
        '.qty-cart'    => $this->renderPartial('@qty-cart.htm', ['qty' => count($this->getItems())])
      ];
    }

everything works fine, when I click on the button, a product object is added to the session, and everything is updated and rendered.
But I need to be able to delete one item from the cart by clicking on the Delete
button. There is a Delete button, on it data-request="onClearOneItemCart"
Below is onClearOneItemCart itself

public function onClearOneItemCart(){
       foreach ($this->getItems() as $key => $value) {
         if($value->id == Input::get('id')){
           Session::pull('cart.'.$key);
         }
       }
       return [
          '@.cart-items' => $this->renderPartial('@cart-item.htm')
       ];
     }

here I loop through the session and look for the desired object to be deleted by its id
. Everything also works, but it is deleted only after a reboot, and I need it to be deleted and rendered immediately.
Please tell me how to implement?