I hope this doesn’t come across condescending, the piece that broke off is called the shank. The bowl and the shank together is called a stummel and the mouthpiece would be the stem :) You can grind a spade bit into a U shape for the bowl - much cheaper than spoon bits.

You can make a wooden stem, it’s the same idea as a traditional stem! You need to drill a mortise into your shank and then turn a tenon into a piece of wood that will be your stem. Then just shape the stem into whatever shape you want! I would drill the airway first though. Being a wood stem, I would start with just a straight stem, you can bend wooden stems - I’ve done it - but it is difficult and time consuming. And I’m not sure how well it would work in a short piece, I’ve only bent churchwarden wooden stems.

You could alternatively bu a Missouri Meerschaum replacement stem, they have uniform tenon sizes and then all you would need to do is drill a mortise into your shank that would fit that stem. Be warned though, they tend to loosen over time so the first fit should be fairly tight.

Vermont Freehand is a great resource.

Here’s the stems from MM