Since you can follow the details on how to build the panjolele at the aforementioned link, I won't cover the process but rather describe some of the extra bits I did along the way.
For achieving the design on the cake pans, I used a metal staining product called Sophisticated Finishes (which found on clearance at Michaels- what luck! ). First, I sanded off the non-stick coating using some regular coarse sandpaper, and then I applied the stain with a paint brush. I used the Blackened Bronze stain, and it was dry within an hour or so.
After spending some time cooking up a design on the computer (I used Artrage as my tool of choice), I then ran down to our local Fab Lab to make use of their laser engraver. The laser engraver simply took the stain back off of the pan, revealing the original metal color underneath! I finished the pans off by spraying them with some clear coat as recommended by the Sophisticated Finishes product. I will post the image I used to engrave below in case any of you might want to use it.
One other added touch, was the stained nut and fret markers. Since I didn't happen to have any wood stain handy, I improvised by just using a few orange/red Copic markers on the wood. I think it turned out pretty well!
Here is a video of me and my humble ukulele playing skills to show off the sound of the panjolele. It has a great mix of jangly banjo sound mixed with the relaxing tones of a classic uke.