S
You will want to bring back a backup copy of the file at Steam\userdata\\7\remote\serverbrowser_hist.vdf.
Note that if you just replace the favorites list in Steam\userdata\\7\remote\serverbrowser_hist.vdf with your backup and restart Steam, it just gets replaced with the newer version with everything cleared. That's because remotecache.vdf has a hash, time, and date of the newer file and asks Steam for that newer copy when it finds an old copy of our file.
In order to tell Steam that we actually have the newer copy, we'll need to exit Steam and "touch" serverbrowser_hist.vdf so that Steam believes that it was just modified and that it needs to sync with the cloud to upload those changes. To do this, open Command Prompt and type this in to go to the folder that contains serverbrowser_hist.vdf:
cd C:\Program Files (x86)\Steam\userdata[your id]\7\remote
After we go to the folder, we'll update the "date modified" time to the current time:
copy serverbrowser_hist.vdf /B+ ,,/Y
Start Steam, and you're all set!