This plugin uses WordPress + Varnish and caches the sidebar with ESI.
This plugin uses Varnish and ESI to cache the sidebar separately from the page and aggressively uses Purges so that you can set long expire times without worrying about comments and post edits not showing up immediately.
I did a presentation on the methodology behind this which explains how the plugin works. Blog Post
Should you use this?
If you're on a Virtual server, it is likely that you won't be able to install Varnish or run your site behind it. If you are able to run Varnish, the use case for this plugin is a little different than WordPress-Varnish.
If you are trying to cache your site where your visitors are hitting one or two pages and you don't get many comments, WordPress-Varnish will result in faster pageloads.
If your site is dynamic and you receive a lot of comments, or, your visitors are likely to surf multiple pages rather than a single landing page, using ESI will probably provide enough benefit to make the plugin worthwhile for you.
Image used under Creative Commons License from Varnish Software.