You can get a browser that can receive commands from the socket, such as uzbl, luakit or dwb.
You can add this function (listening on a socket or even a file) with the extension (add-on, plug-in, regardless of what your favorite browser calls it).
You can insert some javascript on the page that you are editing, which will make it reload some signal that you can control from the CLI.
You can write a script that will kill the browser and open it again. Some browsers will try to load the cached version of the page. To do this, you better use the query string and create a unique URI each time (for example, open "foo.html?$(date +%s)" ).
The possibilities are endless!
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