The simplest hardware-wise is:
Just one small chip with its bypass cap.
The internal pullup on GP0 is enabled, so GP0 will be low when the switch is closed and high when open. The rest is firmware. At its simplest, the firmware can just produce a fixed size pulse on GP1 whenever it sees a transition on GP0. However, unlike dedicated analog solutions, you can apply different policies that might be useful. For example, when a pulse turns off the system, this could enforce a minimum time to let the system fully shut down before attempting to start it up again.