This is done because, generally speaking, the icons that websites provide are smaller than the icon size used by Windows. Therefore, white space is added to increase the dimensions of the icon.

The only way to increase the icon size would be to manually download the icon file and change the icon that the shortcut uses.

The easiest way to download the icon file is to use a service like Favicon Grabber to get it from the website. Alternatively, you can view the website's HTML code and find the file path that way, but that requires some coding knowledge.

Note About Favicon Grabber: I've found that sometimes the download button will give you a 404 error page. To get round this, right-click on the icon preview and click Save Image As to download it.

Once you have the file saved, you need to right-click your shortcut on your desktop and click Properties. Under the Web Document tab, press the Change Icon... button. Then browse to your icon file to set it.

Hope this helps.

Some websites provide a favicon in more than one format. You would have to stretch the icon in width and height to fill the full available space.