Quote ThomasAlva, "Incidentally, how would you make it in a Bridgeport? Would you have to get a special radius endmill?"

To do it in the Bridgeport, you would make the 7/8" holding piece out of square stock instead of round. Put the concave radius in it, then reclamp it in the vice with the radius part up and plumb. Pick up the center of the block and set the dials to "0" in both directions. Then glue the 1"dia stock into the radius like before. Then you use a boring head in the spindle with the cutter facing inward instead of the way you would to bore a hole. Then you use the boring head to "reverse bore" the 1" part until its round and to size. A boring head can also be used for making the radius in the 'holding part', if you don't have a 1" end mill.

This trick part you show was one of the things we made in high school machine shop class. It was used to teach you to work/think outside the box. We used steel and solder though. And using cyanoacrylate to hold things together was used a lot where I worked before retiring. Parts for molds that needed to be perfectly matched in shape but had to be two separate parts to split at a parting line.

You could use a belt grinder to remove some of the excess stock on the 1" piece, if your not comfortable with interrupted cuts.