"Internet Explorer has stopped working" when selecting F12 Developer tools for a specific site

In my case I had a CSS (font-awesome) file included twice on the layout.cshtml file causing IE to crash every time I press F12.

Removing the duplicate fixed it:

<link rel="stylesheet" type="text/css" href="~/Content/themes/base/css/font-awesome.min.css" />

This bug has been reported to Microsoft and a demo is linked on the page. The Microsoft Edge Team provided the following statement:

Thank you for the feedback. This appears to be fixed in Edge as I am not able to repro this. Please note that we are not working on IE feature bugs any longer unless they are security related. As a result this item will be closed out as not repro to reflect the testing results from Edge.

It doesn't look like we'll see it resolved by Microsoft.

My laptop has 2 graphics processors: an integrated one and a a higher end nvidia one. For me the solution was to force IE11 to use the nvidia gpu. You can do this in windows by going start and searching for 'Graphics Settings'. In there you can add both the x86 and x64 iexplore.exe files and set the to 'High Performance'. Once I did this IE11 no longer crashed when I pressed F12.