Power controlling a soldering iron
The best solution I think is to use a light dimmer circuit. You can buy it already assembled (look one for 60 W) and it is plug 'n play. What they do is almost a PWM on the AC signal from the grid using a triac.
If you want to build it yourself, it is very simple, though I see no point on building it other than just for fun:

Image source: Circuits Today: Diac Applications, Triac Lamp Dimmer Circuit
Where there is the lamp you should put your soldering gun.