The top and bottom rail both get rabbets for the mirror and backer board to fit into. The top rail has an extra wide rabbet because most of it is going to be cut away to form the top arc. Rather than pay extra for a curved top edge on the mirror, I’ll just curve the wood instead and the effect will be the same.
The bottom rail gets a groove in its face to receive the tongue of the shelf.
The left and right stiles get a stopped groove to receive the tongued corbels. I chiseled a small mortise at the end of the groove, used my plow plane to clear out most of the wood, and finished up with the router plane to get everything to the correct depth. I experimented with a little stop block to help me stop the plow plane before hitting the end of the mortise.
A lot of people just screw their corbels onto their stiles, but that feels cheap to me. Everything else is solid wood construction, so why be lazy when attaching the corbels?
The corbels sit 3/4” lower than the top of the stiles, because the top of the stiles will be turned into tenons which will travel through mortises in the top shelf. Maybe I’ll even wedge them in place. We’ll see.
-- I've been creating problems to solve since I was born.