This is a pain, but the best solution I could find is to

Open the cookies folder, which for me is at the link below. (Be sure to change username to your own:

C:\Users\username\AppData\Local\Packages\Microsoft.MicrosoftEdge_8wekyb3d8bbwe\AC\#!001\MicrosoftEdge\Cookies

You can view the cookie contents and domain in a text editor like Sublime Text (3rd party) or Notepad (Included with Windows)

A text editor like Sublime Text allows you to open them all at once and search within the files. It presents a summary and one can then delete the cookie for the site they wish to delete cookies for. There may be other tools out there, but this is what worked for me to get rid of a certain cookie.

And I for one will absolutely be putting in a feature request as per Microsoft's answer.

Hello,

Thank you for posting in Microsoft Community.

I understand that you are trying to delete the particular cookie in Microsoft Edge. We will assist you.

This option which you are searching in Microsoft Edge is unavailable, I suggest you to leave a Feedback in the feedback app. You may simply search for “Windows Feedback” from the search box, or give your feedbacks on the  Microsoft Edge.

Refer: Updates and feedback 

Keep us posted if any further issue on Windows.