DNS resolution works for nslookup but fails in browser while using openconnect
Thanks to this answer: https://superuser.com/a/86245/356729

The command


  networksetup -setdnsservers Wi-Fi 10.66.0.1, 10.66.0.2


solved the problem. When I disconnect, I also have to manually restore settings using:


  networksetup -setdnsservers Wi-Fi 192.168.100.1