My friends have a small fruit orchard on their property and have accumulated a rather large pile of branches from pruning their trees every year. Orchard prunings are a great source of small diameter branches of a lot of nice species - that's where these short pieces of wood came from. The orchard contains pear, apple, persimmon and cherry trees. It's hard to say exactly what kind of wood this particular handle was made from since they were all just in a big pile and I'm not very skilled at fruit tree wood identification. Any hardwood will work - chose something you like.
The hardest part of the whole project was probably removing the old black plastic handle. Held on with a long bolt inside of the handle, it was extremely difficult to remove using a socket wrench since the hole in the handle where the bolt was located was so small that it did not allow the socket to fit inside. I have heard of thin-walled socket heads, which might have fit down the small hole, but I don't have any at my shop. No matter, I simply cut off most of the handle exposing the bolt much closer to the source, thus making it easy to get the socket head on to remove.
Once the old handle was off, we gathered up a hand saw, the wood and some whittling knives and set out to select a piece of wood that had a sufficient diameter to accept the mounting shaft on the portafilter. We came up with the candidates in the photo above.
To continue with the project we also ended up using:
angle grinder with sanding disk
random orbital palm sander
sand paper for hand sanding
chisel and drill press to cut the mortise in the handle
"Good Stuff" rub on varnish