If the dashboard is in the same sitecollection you can use the ContentByQuery webpart. It works like the search webpart but queries the lists directly. The drawback is that it fails if you have too many lists and too many items. If the webpart is missing on your site. You need to activate the publishing feature on the site and on the web. Then you will find it in the Content Roll Up group.
One alternative is that you have a webjob running in Azure, checking for new webs and updates a common list on the dashboard web.