When you say nook, is it an actual nook with walls on three sides? I imagine it would not be very difficult to attach a supporting structure around the walls fixed through to the studs and mount the desk surface over it. If the desk is to float from only one wall that's a bit more complicated, and might depend on what weight it needs to hold.

It is a nook with 3 walls. I would like a floating desk mounted with sliding draws on the underside. The desk material to be a close match to ceaserstone oyster as that is what is in the kitchen

Can you ask the kitchen installer to do it?

Builder won't allow work to take place until the house is finished

Build your desk with either brackets or a piece of timber firmly attached to the studs, then screw bench onto the support beam.
If you are requiring draws, these could be built in as well and support the bench.