Depending on what you mean by 'handmade' either no one that I know of or Carl Goldberg / CEGO.

He will make boxers to spec but uses machine stitching. 

I wouldn't go in there and take an hour of his time (if he's busy) to order a single pair of boxers - i.e. it isn't his main business - but he can hook you up.

I have been accused of narcissism but boxers that matched my shirts never did anything for me. Knits are more practical.

handsewn boxer shorts?
You have to be kidding me.

I can make a boxer short to spec. Meaning sizing and details. to have one of my own tailors make such a garment vs having them made in the factory that dose my work, will be much more expesive.
It can be done.
I have made tie backs.

voiles
silks
covered waistbands.
no elastic.
etc.

Carl

Our friend Biff has inspired a reconsideration of what "handmade" means. Just because boxers are no longer made like they were in the Bronze Age doesn't mean they're not handmade.

http://www.askandyaboutclothes.com/forum/showthread.php?t=65454

Thanks for the kudos, gents. I'm happy to share when I can.

Some of the discussions on that particular board have "inspired" me (for lack of a better term). I'm thinking of an interactive display set up at a trunk show, like Sartorial Excellence.

One suit will be completely hand-made, one will be made using my 'machined bespoke' method, and the last will be fused. All of them will be made in precisely the same fabrics, and will be lined up, side-by-side.

The fun begins when I hand a participant 3 tent cards with prices on them and ask them to 'pin the tail on the donkey', as it were. I'm interested to see how many will get it right.