Dates in Recent Changes are showing up in non-localized UTC

(Bug, Investigate , Priority: High, Test Status: No automated tests yet , Reported By Bad Link: Thing 3y284oe not found, )
Summary: That is, Eric noticed that something was showing up as having been published 5/31, when it was actually published 6/1 his time.
In principle, these dates (and indeed, all date/times) should be localized to the viewer's timezone.
Need to design how this will work. Do we handle it server side (by taking the timezone from the RequestHeader and adjusting as we display)? Or do we handle it client side (by putting the encoded timestamp into the page, along with a rendering hint, and actually rendering the date/time in the client)? Either is plausible, and it isn't clear which is harder.
Keep Anonymous in mind with this: the timezone should be based on the browser's time, not anything magical about the User.
Keep the static page view (for crawlers) in mind for this. Those don't really have a "browser", which may argue for server-side rendering.