When navigating to a site with an expired SSL certificate, Brave Private sessions (and Chome and Edge) warn “Your connection is not private” and also offer a link titled "Proceed to ". This is expected and good behavior. Brave’s normal (non-private) sessions are the only ones that do not offer the “Proceed to” link. I am confident this is an oversight and needs to be reintroduced. Please note: works in Private mode; broke in normal mode.
All the URLs through which I encounter this problem are part of my company’s intranet. (IT understaffed; we are working on it.) I am confident you can find or create a server that will present the issue.
The issue presented on the Version 1.25.70 Chromium: 91.0.4472.77 (Official Build) (64-bit). Same results with shields up and down.