I had a similar need and ended up writing a script that queries the Jira API for every project key. You can use the query below to get the most recent issue update for a project with key "PROJ" for example. It will return 1 result with only the "updated" date field of the most recently touched Jira issue for that project.
It will be hard. You can write a script that is running trough all projects and is comparing the data of the last updated ones. Or if you can somehow order Issues in project by Updated Time and grab the newest one, this would be easier.
But I do not have a ready script for that.
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