In Batman V Superman it's shown that Batman brands criminals with a 'bat brand'.
This brand on someone means they will definitely be killed. Why does he choose this instead of killing them himself or not doing it at all?
There is very good fan interpretation about it on reddit
I am sure someone has made this connection before, but...
In the opening scene, the cinema that young Bruce and his parents come from was showing "The Mark of Zorro".
Zorro, a proto-Batman style vigilante, is known for branding his enemies with his Z-symbol.
Therefore, Bruce was obviously heavily inspired by Zorro, and 20 years into his career, when setting his "new rules", Bruce decided to adopt the idea of marking criminals with his own logo, just like Zorro.
And even quite famous fan interpretation of the reasoning behind bat-branding, appreciated on moviepilot.com too.