how to "float" a large desk (3000mm x 720mm x 40mm) between walls
A solid wood plank 40mm (1-9/16") thick probably isn't stiff enough to span that distance (just under 10' for the Yanks) without substantial bounce. It'll be strong enough, but you would get seasick working on it and it would sag over time and with heavy loads. 

Now, if you made it thicker, say 55-60mm, and you beveled the front edge to give the illusion of a thinner surface, you'd have something workable. You could support it solely on the rim cleats you describe and have a fairly stiff top. 

The alternative is to go with your 40mm thick dimension and bolt several steel angles to the underside, back just far enough that they aren't conspicuous. I'd suggest a 50mm angle. Start with two and add more if needed. Steel is fairly flexible itself, so quantity is in question. These would not need to rest on the wall cleats to serve their purpose if they're securely fastened to the top. They could end just short for convenience.