That is a pretty deep shelf! Let me tell you what I have done a couple times for customers.
This was shelving about 1×6 run around the room at the top of door level. I used stock corbels to support the shelf. Unfortunately these are a bit expensive. If you have the tools – bandsaw and router – you can make your own.
The trick was to fasten metal angle brackets firmly to the wall (into studs) and then rout out the back and top of the corbels to fit around the metal brackets and cover them. I had to remove the wall plaque on the back of the corbel to get it out of the way. Once you have the corbel cut to fit around the metal bracket, screw down through the shelf, through the metal bracket, and into the corbel.
The beauty of this method is that the metal bracket is actually supporting the shelf, but it is covered by the corbel and you never see it.