This is a Greasemonkey (Tampermonkey) userscript that will activate on the Outlook Web application site and add a badge showing the unread mail count.
The count is computed extracting the numbers from the favorite folders, if you would like to match all flolders you can modify the computing function accordingly.
The library used to render the badge is http://lab.ejci.net/favico.js/, you can find the customization options on the homepage of the aforementioned library.