Hey there
Here's a quick and dirty method that works well, If you have access to a table saw:
acquire some slats of good hardwood such as oak ash or hickory which are around 1/2" to 3/4" thick and about 1.5 to 2" wide.
Mark center lengthwise on your 2 halves and adjust the fence of the table saw for this. Lower the saw blade so that it cuts about 1/8" or less into your slats.
The next step is to take your 2 halves, glue and clamp them together..it helps if you have something metal such as a coat hanger in the channel to prevent glue from getting in.
After the glue has dried, you have a workable handle blank to rasp, carve and sand into a pipe hawk handle.
If you want to make a pipe hawk stem from a solid piece, it REALLY helps if you start with a chunk of wood which is perfectly square. This way you can mark your center points with accuracy, and the wood is held perfectly straight in a vise for when you drill pilot holes on either end.
After your pilot holes are drilled you can either burn out the channel on either end (a length of 1/4" mild steel rod flattened like a screw driver on the end and heated red hot works great!) or you can use a long drill bit to bore into the hole alternately from either side.
Remember that if the holes on either end are center, it doesn't matter so much if your holes don't meet up exactly in the middle of the handle.
I really hope this helps
Take care
Iain