How to restore Parallel's Applications folder?
The way I was able to resolve the issue is by launching Parallels and then going into the "configure" settings. Next, I went to the Options > Applications, and checked "Show Windows applications folder in Dock".

Apparently when you drag the folder out of the dock, it will automatically uncheck this setting for you. In fact, if you try adding the folder manually and then launching Parallels, it will automatically remove the manually added folder.