Wall bracket assembly
We started by cutting one-inch square steel tubing with an angle grinder. This piece becomes the wall bracket that mounts to the wall and holds both the shelf and the toilet paper rod. Using a bandsaw, we cut one face off the square tube to create a "C" channel (pre-made C-channel steel would let you skip this step).
On the drill press, we drilled two holes on the face opposite the opening for wall mounting, and two holes on the adjacent face to secure the wood shelf, then deburred everything with a 120-grit flap disc on the angle grinder.
Creating the toilet paper rod
We sketched a holder design on scrap plywood and added screws along the inside profile as anchor points. Using a ¼" aluminum rod, we clamped one end to the fixture and bent the rod around the screws to match the shape. We drilled out a coupling nut so the rod slides through smoothly, then hammered the end into a mushroom head to stop it from sliding off, before welding the whole assembly to the mounting bracket.
Wood shelf
We cut a piece of walnut to roughly 3" wide, 8" long, and 1" thick with a miter saw, applied sealer wax to the walnut, and sprayed clear coat on the steel bracket for a modern finish.
Installation
Screw the mounting bracket to the wall, then slide the wood shelf into place and secure it from underneath. The finished piece has a slip-on toilet paper holder and a handy little shelf for phones, candles, or whatever else belongs in a bathroom.