The issue is that cpanel from the https://domain.com:2083 looks like its missing css or files…
Symptom:
You try to access your cPanel behind CloudFlare and are finding that on the first page load that no images (or stylesheets or javascript) load – and, when trying to navigate to any link, you are immediately logged out. The experience is as if cPanel were broken in some way.
Cause:
cPanel has an option called “Cookie IP Validation”. This setting checks that the IP address that the visitor originally came from matches their IP address on subsequent requests. With CloudFlare, the IP address for requests to your server can variably come from any IP address in the list at https://www.cloudflare.com/ips
Resolution:
To resolve this issue, in your WHM, navigate to “Tweak Settings” -> “Security” -> “Cookie IP Validation”. On this screen, set the value for “Cookie IP Validation” to “disabled”. After this, loading your cPanel WHM interface through CloudFlare should work as expected.
Other resources:
https://forums.cpanel.net/threads/cpanel-looks-stupid-when-i-log-in.266321/
https://support.cloudflare.com/hc/en-us/articles/200169276-How-do-I-use-cPanel-with-CloudFlare-