Floating wall mounted office desk
Your issue is less about how you'll fasten it to the wall, and more about the stiffness required to span that width. I have a very similar desk in my office made of repurposed 1-3/4" thick veneer and particle board door slabs hung only on cleats fastened with 3-inch construction screws. My situation is actually L-shaped, with one slab hanging from the other, and it's suitable for a multi-station computer desk.

2 inches of solid or engineered wood will be strong enough, but it will bounce a bit. I'd estimate the weight at around 100 lbs. It doesn't take much to support that, plus maybe another 50 lbs. of equipment. 

I'd run cleats around the 3 sides. They can be almost anything of wood or metal. Even 1x4 pine would do, as long as you get appropriate fasteners into the masonry and wood framing. If you taper the front ends they'll be much less conspicuous. 

I'd then install a large steel max-bracket (or two) in the center from the rear to stiffen the front of the desk. It should extend at least 2/3 the depth of the desktop. It'll be practically invisible to anyone standing nearby. Be sure to use sufficiently large lag screws here. There will be a substantial pull-out force on the upper bolts. 

This arrangement will be strong enough to support the desk, your computer equipment or whatever, and the backside of any overly-casual, average sized colleagues who wander by.