Undercutting behind a thread is going to require interpolation so a CNC mill will be necessary. As for the cutting tool these guys are my go to for such applications:
https://www.harveytool.com/You don't have to have a CNC for that. On a lathe it is relatively simple to use a trapezoidal cutter on a boring bar to do it. Set the angle of the blade for the angle of the seat, move it down the axis of the hole inside the threads, then bring it (radially) out at the bottom of the hole and finish the cut. Then reverse to get the cutter back out.
It takes some planning and attention to the geometry for your depth, but can be done manually by someone with moderate skills.
It would take some thought on how to do it with a mill unless you had a few extra axes to play with.
