Install and run fiddler. It will do everything automatically.

Edge browser seems to pay attention to the interface you are using to access your sites. My guess is that you are using Vagrant to launch a Virtualbox VM. My answer below assumes that you are accessing via a Virtualbox host-only network, or some other network interface that has an NdisDeviceType of 1.

What didn't work

None of the following worked for me:

1. Using about:flags and confirming that "allow localhost loopback" was on

2. Control panel, Network and Internet, Internet Options, Security and adding my site explicitly to Trusted Sites or Local Internet.

3. CheckNetIsolation LoopbackExempt -a -n="Microsoft.MicrosoftEdge_8wekyb3d8bbwe"

My environment

In my case, I have VirtualBox 5.2.18 running on Windows 10 build 1803 "Spring Creators Update". Using Edge 42.17134.1.0. I have a host-only network for my VM guests. e.g. 192.168.7.0/24. I couldn't access addresses from my Edge on the VM host such as http://192.168.7.0. This site was hosted by a web server running in my VM guest. Note that this address worked just fine in Google Chrome, Internet Explorer 11 etc.

What worked

The solution is as follows:

1. Find the interface number for the host only network. I ran "route print" from the Windows command line and the first number shown in the "interface list" in my case was 17.

2. Use regedit to change the interface type from 1 to 0. The key is:

   HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Class{4d36e972-e325-11ce-bfc1-08002be10318}\XXXX

In my case XXXX was 0016 because my interface number was 17. I had to change *NdisDeviceType from 0 to 1. The * in that key name is a literal asterisk. I had to reboot for the changes to take effect.

The answer was gleaned from a post by "Jani L" dated Oct 3, 2017, on the first URL referenced below, but it didn't give a clue as to how to determine the interface number. The second reference below was the thread on which I originally posted this solution.

References:

https://developer.microsoft.com/en-us/microsoft-edge/platform/issues/10142843/

https://social.technet.microsoft.com/Forums/en-US/0face535-3c7a-4658-be34-6c376322ca34/microsoft-edge-cant-open-local-domains

https://www.virtualbox.org/ticket/15565

It seems you are using Laravel Homestead box. If so, you can forward one of your host ports to the 80 port of your VM. Thus, you will be able to access your web sites hosted on your VM on MS Edge.

Here is what I've done:

ports:    - send: 8000      to: 80

If you don't want to have to type yourdomain.dev:8000 you may use fiddler. Thus, you will be able to only type yourdain.dev. :D