Do it from the hamburger menu 
Often they will tailor themselves to permit well known browsers like Chrome, Edge, Safari, and Firefox. While Brave is getting to be well known, it’s still kind of “small fish” in the pond in terms of awareness. So they could block Brave or parts of it because they haven’t tailored everything for it.
Examples of where people have experienced issues because of Avast: (the first one might be similar to your current)
Why does my Brave crash every like 2 weeks and unlogs me from every website? - #6 by WindowOpener
"Security" problems when connecting to https-sites
Privacy error https - #10 by machinist60
Can't access Steam website with Brave - Google chrome works - #3 by Potato12
Can't access safe sites; keep getting blocked - #12 by NonyaBeeswax
There’s been a lot more, but those are ones I could pull up from quick search.
Well, if find out it’s Avast then you’d have to find out what particular settings. Such as if you have it running a cleaning option like one of the other people did, then you’d disable the cleaning and just would use it for virus only. But whatever setting is creating the conflict, you’d have to find and reverse. Or you’d be able to contact Avast and have them work with you to get things resolved. Worst case scenario, maybe consider a better antivirus…though I doubt it would have to come to that.