There are a lot of ways this could be done, but I decided to leverage the work I have done in other projects, so the design is an opto-isolated triac AC power switch controlled by an ATTiny45.
The ATTiny needs a 5 volt power supply, so that requires an isolated AC/DC power supply module - ironically the most expensive component of the entire build. The ATTiny45 is set up with one of its I/O lines connected to a button (other side of the button to ground), and a second as the opto-isolator driving line. There will be a pilot light hooked up to the output to act as a power indicator. If you're still working after a half hour, the light will go out and you can push the button to get another half hour. You can also always push the button twice to briefly turn it off and on and reset the half hour timer.
The triac circuit is one half of the Toast-R-Reflow power switching board. It uses a MOC-3020 opto-isolated triac driver and a BTA-20 triac. The board in this case is routed for a design maximum of 200W. At that sort of power, the BTA-20 will only be expected to dissipate about 2 watts of heat, which should be easy to sink through the enclosure.
As with all HV designs, care must be taken to insure the correct current capacity for the load-bearing traces and to pay heed to creepage and clearance distances. It's also a good idea to draw a solid divide between the HV and logic portions of the circuit, with only isolated components allowed to bridge the line.
For the chassis, there will be a panel-mounted IEC C14 inlet, plus an NEMA 5-15 outlet. The hot and neutral lines of each will go to dedicated connectors on the board. The pilot light will be wired separately to the outlet hot and neutral. The two grounds will be tied together and to a lug on the chassis. The button mounts at some distance away from the AC connections and ties to the logic part of the board.