Internet Explorer is still part of Windows Server with Desktop Experience. However, it is technically out of date, which means it cannot run modern web applications like Windows Admin Center.
Edge Chromium as a separate download ^
Since the first generation of Edge did not exist on the server, the Chromium version now fills this gap. To date, however, it has not been included with the installation media of Windows 10 or the server, so you have to download and install the browser yourself.
On a server with a desktop, the procedure is the same as on a client OS. Under Server Core, which is also one of the supported platforms, some additional steps are required.
It starts with the fact that there is no browser available to download the installation files for Edge. A download via Invoke-WebRequest is difficult because there is no permalink for specific versions.
Instead, you have to choose the desired Edge release, selecting various criteria using a form on the download page. You can do this on a workstation, then copy the MSI file to the server and execute it there. I recommend downloading the complete offline installer right away.
Incompatibility problems ^
If you decide, as usual, to get the version of Edge that Microsoft designates as current, you will receive the following message when installing it under Windows Server 2019 Core:
Microsoft Edge works best with the latest Windows Updates. Once you download updates and restart your device, rerun the installer.
As it turns out, you can install as many Windows updates as you want. The Edge setup will always show this dialog and then cancel the installation.
Also, switching to the online installer does not help; it will end the same way. It does offer a Get Updates button, which promises to remedy the situation. But if you click on it, nothing happens.
As is so often the case with Microsoft, this is a misleading error message. The problem is that only version 79 of Edge can be installed on Server 2019. If you do so, then your setup will run smoothly.
Launching the web browser ^
If you then want to start the browser, you can, of course, only do this from the command line. Using PowerShell, enter the following:
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& 'C:\Program Files (x86)\Microsoft\Edge\Application\msedge.exe'
Unlike Internet Explorer, there is no Enhanced Security Configuration for Edge that prevents the user from opening pages from the internet zone (Edge does not even know this zone concept at all). However, a responsible administrator will limit the use of the browser on the server to the necessary tasks anyway.