A small repair such as eyeglass frames should be a job that many RCMers could perform fairly easily.
The manufacturing process is most likely a machine that passes electrical current through the contact area of two pieces of thin frame material. The current generates very localized heat, and the hard silver solder/braze material joins the two pieces. The joint cools quickly after the current is switched off, so the brazing is done almost instantaneously.
A way to improvise an electrical resistance heating machine may be possible with some equipment that many metalworking enthusiasts may already own.
A bandsaw welder could very likely be adapted to pinch the pieces together and apply enough heat to the junction for brazing. It would probably require fabricating a couple of copper contact tips to be held in the clamps for the blade. Many blade welders have a low-power setting for annealing the blade after welding has been accomplished. The annealing heat level would be more than adequate to reach the heat level required to braze the eyeglass frame parts together.
A resistance-type spot welder may be another option for the small eyeglass frame parts brazing. If the spot welder has a selector switch to bypass the automatic cycle timing circuit (manual over-ride), or if the operator can figure out how to accomplish the bypass, the S-W machine should be capable of heating the joint into the heat range of brazing with hard silver solder.
Since the OP's parts were previously brazed, the process may work very well by just reflowing the existing braze material with a little flux, although adding a small sliver of silver solder and flux may be required after a thorough cleaning of the joint (and perhaps strengthen the joint if it was weak).
Some MIG welders (and others) have the capability of heating steel to red heat with a carbon rod held in the gun assembly/torch (for autobody heating/shrinking). An older Solar/Century model that I bought several years ago covers this procedure in the users' manual, and came equipped with the torch adapter and carbon rod. The rod is kept in contact with the metal (no arc) and can be moved around in an area for wider heating.