The basic schematic that Gus drew is on Zebra50's (new) site.
While the circuit obviously works well in the Brauner mics, I think it's not too hard to improve it in some respects. Gus gave some good hints already in the old thread. The circuit is pretty linear, so if you like the Brauner sound it's probably not because of the electronics but because of the capsule.
If I were to build a similar mic with an available capsule (such as Tim Campbell's) I would include a DC/DC converter as it makes you less dependent on a solid P48 supply. Also, I suspect the Brauner (MBHO) capsules may be designed for less polarization voltage than the usual 60V. I know that MBHO did special low voltage capsules back in the 70s (in fact I own some of those) and the FET Brauners are very low noise despite the lack of a DC/DC converter.