Edit elements in the jsdom window and save the window as a new HTML file?

Here's an example of how to do it. I've based it on your code but simplified it a bit so that I'd have code that executes and illustrates how to do it. The following code reads foo.html and adds the text modified! to all p element and then writes it out to out.html. The main thing you were missing is window.document.documentElement.outerHTML.

var jsdom = require("jsdom");
var fs = require("fs");

fs.readFile('foo.html', 'utf8', function(error, data) {
    jsdom.env(data, [], function (errors, window) {
        var $ = require('jquery')(window);
        $("p").each(function () {
            var content = $(this).text();
            $(this).text(content + " modified!");
        });

        fs.writeFile('out.html', window.document.documentElement.outerHTML,
                     function (error){
            if (error) throw error;
        });
    });
});

There's no jsdom.env() anymore, and I think this example is easier to understand:

const fs = require('fs');
const jsdom = require('jsdom');
const jquery = require('jquery');

fs.readFile('1.html', 'utf8', (err, data) => {
    const dom = new jsdom.JSDOM(data);
    const $ = jquery(dom.window);
    $('body').html('');
    fs.writeFile('2.html', dom.serialize(), err => {
        console.log('done');
    });
});