For me in Windows 10 x64, Brave always fires up on the left of my two identical monitors. Brave is the only browser that does this: all other browsers (and other apps) remember which screen they were last used on and start in the right place accordingly.
I’ve tried moving Brave to the second monitor, resizing it, maximizing it there and closing it. This doesn’t make any difference, the next time Brave is started it fires up maximized on the left screen. I then have to drag it into place before I can use it.
Graphics card: NVIDIA GTX 1070
Monitors: 2 x 1920 x 1200 LG L246WHX
OS Release: 10.0.17134
Update Channel: Release
OS Architecture: x64
OS Platform: Microsoft Windows
Brave Sync: v1.4.2