Granite overhang support question.

I need some guidance on how to properly support a granite over hang.

I recently had some 3cm granite counter tops installed. But I need to replace the back side of an L shaped cabinet (i damaged it during demo) and install the supports for a 12 inch over hang.
Here is the cabinet/counter tops.


The 2 black lines are the sides of the cabinet that to go all the way from the granite to the ground with 3/4 inch ply, The red lines just have a 3/4 inch board running across. Here is the side view.

So i wondering what type of support bracket I should use.

I had a piece of OBS plywood hanging around so I had planned to cut it to size (and seal the edges) along with a thin piece of oak plywood as a veneer then useing those for the new cabinet back and added support. Then attach an L or T bracket to the back of existing support beam to support the overhang.

Im really just not sure which type of bracket would be best suited to this application. L, or T shaped, or I could easily sneak a 4x4 behind the exiting support beam and use a flat style bracket..

Thanks in advance.

Attached Images