LOL Desktop shortcut Icon does not scale like most icons

Would it be possible to make it so that the shortcut icon for the Windows desktop scales like the majority of other icons do? I have my desktop icons enlarged, but League does not act like the other icons: it stays a small icon in a large box. I tried fixing it on my own by making an icon from a converted picture... and lets say the white border looked pretty bad and the picture was pretty fuzzy.